JEE Main & Advanced Mathematics Mathematical Logic and Boolean Algebra Question Bank

done Boolean Algebra Total Questions - 31

• question_answer1)
  In Boolean Algebra, the zero element ?0?
  A)
                  Has two values  done clear
  B)
                  Is unique done clear
  C)
                  As at least two values    done clear
  D)
                  None of these done clear
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• question_answer2)
  In Boolean Algebra, the unit element ?1?
  A)
                  Has two values  done clear
  B)
                  Is unique done clear
  C)
                  Has at least two values  done clear
  D)
                  None of these done clear
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• question_answer3)
  In a Boolean Algebra B, for all x in B, \[x\vee x=\]
  A)
                  0              done clear
  B)
                  1 done clear
  C)
                  x              done clear
  D)
                  None of these done clear
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• question_answer4)
  In a Boolean Algebra B, for all x in B, \[x\wedge x=\]
  A)
                  0              done clear
  B)
                  1 done clear
  C)
                  x              done clear
  D)
                  None of these done clear
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• question_answer5)
  In a Boolean Algebra B, for all x in B, \[x\vee 1=\]
  A)
                  0              done clear
  B)
                  1 done clear
  C)
                  x              done clear
  D)
                  None of these done clear
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• question_answer6)
  In a Boolean Algebra B, for all x, y in B, \[x\vee (x\wedge y)=\]
  A)
                  y              done clear
  B)
                  x done clear
  C)
                  1              done clear
  D)
                  0 done clear
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• question_answer7)
  In a Boolean Algebra B, for all x, y in B, \[x\wedge (x\vee y)=\]
  A)
                  y              done clear
  B)
                  x done clear
  C)
                  1              done clear
  D)
                  0 done clear
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• question_answer8)
  In a Boolean Algebra B, for all x in \[B,({x}'{)}'=\]
  A)
                  \[{x}'\]  done clear
  B)
                  x done clear
  C)
                  1              done clear
  D)
                  0 done clear
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• question_answer9)
  In a Boolean Algebra B, for all x, y in B,\[(x\vee y{)}'=\]
  A)
                  \[{x}'\vee {y}'\] done clear
  B)
                  \[{x}'\wedge {y}'\] done clear
  C)
                  1              done clear
  D)
                  None of these done clear
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• question_answer10)
  In a Boolean Algebra B, for all x, y in \[B,(x\wedge y{)}'=\]
  A)
                  \[{x}'\wedge {y}'\]          done clear
  B)
                  \[{x}'\vee {y}'\] done clear
  C)
                  1              done clear
  D)
                  None of these done clear
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• question_answer11)
  In a Boolean Algebra B, for all x in B, \[{0}'\] is equal to
  A)
                  0              done clear
  B)
                  1 done clear
  C)
                  \[x.0\]   done clear
  D)
                  None of these done clear
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• question_answer12)
  In a Boolean Algebra B, for all x in B, \[{1}'=\]
  A)
                  0              done clear
  B)
                  1 done clear
  C)
                  \[x\wedge 1\]   done clear
  D)
                  None of these done clear
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• question_answer13)
  Dual of \[({x}'\vee {y}'{)}'=x\wedge y\] is
  A)
                  \[({x}'\vee {y}')=x\vee y\]           done clear
  B)
                  \[({x}'\wedge {y}'{)}'=x\vee y\] done clear
  C)
                  \[({x}'\wedge {y}'{)}'=x\wedge y\]          done clear
  D)
                  None of these done clear
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• question_answer14)
  Dual of \[x\vee (y\wedge x)=x\]is
  A)
                  \[x\wedge (y\vee x)=x\]              done clear
  B)
                  \[x\wedge (y\wedge x)=x\] done clear
  C)
                  \[(x\vee y)\wedge (x\vee x)=x\]             done clear
  D)
                  None of these done clear
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• question_answer15)
  Let B={p, q, r, .....} and let two binary operations be denoted by ?Ú' and ?Ù? or ?+? or ?.?, then
  A)
                  \[p\,\vee {p}'=0\]            done clear
  B)
                  \[p\wedge {p}'=1\] done clear
  C)
                  \[p\vee {p}'=1\]               done clear
  D)
                  None of these done clear
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• question_answer16)
  Let B={p, q, r, .....} and let two binary operations be denoted by ?Ú' and ?Ù? or ?+? or ?.?, then
  A)
                  \[p\wedge {p}'=1\]         done clear
  B)
                  \[p\wedge {p}'=0\] done clear
  C)
                  \[p\vee {p}'=0\]               done clear
  D)
                  None of these done clear
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• question_answer17)
  Let B={p, q, r, .....} and let two binary operations be denoted by ?Ú' and ?Ù? or ?+? or ?.?, then
  A)
                  \[a\vee a=0\]    done clear
  B)
                  \[a\vee a=a\] done clear
  C)
                  \[a\vee 1=a\]    done clear
  D)
                  None of these done clear
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• question_answer18)
  Let B={p, q, r, .....} and let two binary operations be denoted by ?Ú' and ?Ù? or ?+? or ?.?, then
  A)
                  \[a\wedge a=1\,\]           done clear
  B)
                  \[a\wedge a=a\] done clear
  C)
                  \[a\wedge a=0\]              done clear
  D)
                  None of these done clear
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• question_answer19)
  Let B={p, q, r, .....} and let two binary operations be denoted by ?Ú' and ?Ù? or ?+? or ?.?, then
  A)
                  \[a\vee 1=a\]    done clear
  B)
                  \[a\vee 1=1\] done clear
  C)
                  \[a\vee 1=0\]    done clear
  D)
                  None of these done clear
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• question_answer20)
  Let B={p, q, r, .....} and let two binary operations be denoted by ?Ú' and ?Ù? or ?+? or ?.?, then
  A)
                  \[a\vee {a}'=0\]                done clear
  B)
                  \[a\vee {a}'=1\] done clear
  C)
                  \[a\vee {a}'=a\]                done clear
  D)
                  None of these done clear
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• question_answer21)
  Let B={p, q, r, .....} and let two binary operations be denoted by ?Ú' and ?Ù? or ?+? or ?.?, then
  A)
                  \[a\wedge {a}'=1\]          done clear
  B)
                  \[a\wedge {a}'=0\] done clear
  C)
                  \[a\wedge {a}'=a\]          done clear
  D)
                  None of these done clear
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• question_answer22)
  Let B={p, q, r, .....} and let two binary operations be denoted by ?Ú' and ?Ù? or ?+? or ?.?, then
  A)
                  \[{0}'=0\]             done clear
  B)
                  \[{0}'=1\] done clear
  C)
                  \[{1}'=1\]             done clear
  D)
                  None of these done clear
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• question_answer23)
  Let B={p, q, r, .....} and let two binary operations be denoted by ?Ú' and ?Ù? or ?+? or ?.?, then
  A)
                  \[(a\vee b{)}'={a}'\vee {b}'\]      done clear
  B)
                  \[(a\vee b{)}'={a}'\wedge {b}'\] done clear
  C)
                  \[(a\vee b{)}'\vee a\vee b\]       done clear
  D)
                  None of these done clear
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• question_answer24)
  Let B={p, q, r, .....} and let two binary operations be denoted by ?Ú' and ?Ù? or ?+? or ?.?, then
  A)
                  \[(a\wedge b{)}'={a}'\vee {b}'\]                done clear
  B)
                  \[(a\wedge b{)}'={a}'\wedge {b}'\] done clear
  C)
                  \[(a\wedge b{)}'=a\vee b\]         done clear
  D)
                  None of these done clear
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• question_answer25)
  Let B={p, q, r, .....} and let two binary operations be denoted by ?Ú' and ?Ù? or ?+? or ?.?, then
  A)
                  \[a\vee (a\wedge b)=a\]             done clear
  B)
                  \[a\vee (a\wedge b)=b\] done clear
  C)
                  \[a\vee (a\wedge b)=a\vee b\]                done clear
  D)
                  None of these done clear
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• question_answer26)
  Let B={p, q, r, .....} and let two binary operations be denoted by ?Ú' and ?Ù? or ?+? or ?.?, then
  A)
                  \[a\wedge (a\vee b)=b\]             done clear
  B)
                  \[a\wedge (a\vee b)=a\] done clear
  C)
                  \[a\wedge (a\vee b)=0\]             done clear
  D)
                  None of these done clear
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• question_answer27)
  Let B={p, q, r, .....} and let two binary operations be denoted by ?Ú' and ?Ù? or ?+? or ?.?, then
  A)
                  \[x\vee {x}'\,x={x}'\]      done clear
  B)
                  \[x\vee {x}'\,x=x\] done clear
  C)
                  \[x\vee {x}'\,x=1\]          done clear
  D)
                  None of these done clear
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• question_answer28)
  Let B={p, q, r, .....} and let two binary operations be denoted by ?Ú' and ?Ù? or ?+? or ?.?, then
  A)
                  \[x\vee {x}'y=x\]              done clear
  B)
                  \[x\vee {x}'y=y\] done clear
  C)
                  \[x\vee {x}'y=x\vee y\] done clear
  D)
                  None of these done clear
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• question_answer29)
  Let B={p, q, r, .....} and let two binary operations be denoted by ?Ú' and ?Ù? or ?+? or ?.?, then
  A)
                  \[x\wedge (x\vee y)=x\]              done clear
  B)
                  \[x\wedge (x\vee y)=y\] done clear
  C)
                  \[x\wedge (x\vee y)=1\]              done clear
  D)
                  None of these done clear
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• question_answer30)
  An OR gate is the Boolean function defined of
  A)
                  \[f({{x}_{1}},\,{{x}_{2}})={{x}_{1}}\wedge {{x}_{2}};\,\,{{x}_{1}},\,{{x}_{2}}\,\in \,\{0,\,1\}\] done clear
  B)
                  \[f({{x}_{1}},\,{{x}_{2}})={{x}_{1}}\vee {{x}_{2}};\,\,{{x}_{1}},\,{{x}_{2}}\,\in \,\{0,\,1\}\] done clear
  C)
                  \[f({{x}_{1}},\,{{x}_{2}})={{x}_{1}};\ \,{{x}_{1}},{{x}_{2}}\,\in \,\{0,\,1\}\] done clear
  D)
                  \[f({{x}_{1}},\,{{x}_{2}})={{x}_{2}};\ \,{{x}_{1}},\,{{x}_{2}}\,\in \,\{0,\,1\}\] done clear
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• question_answer31)
  A NOT gate is the Boolean function defined by
  A)
                  \[f(x)=x,\,\,x\in \{0,\,1\}\]           done clear
  B)
                  \[f(x)={x}',\,\,x\in \{0,\,1\}\] done clear
  C)
                  \[f(x)=x+{x}',\,\,x\in \{0,\,1\}\] done clear
  D)
                  None of these done clear
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