| Input | Output | ||
| \[{{x}_{1}}\] | \[{{x}_{2}}\] | \[{{x}_{3}}\] | S |
| 1 | 1 | 1 | 1 |
| 1 | 1 | 0 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 |
A) \[f({{x}_{1}},{{x}_{2}},{{x}_{3}})={{x}_{1}}{{x}_{2}}{{x}_{3}}+{{x}_{1}}{{x}_{2}}x_{3}^{}\]\[+\,{{x}_{1}}x{{}_{2}}{{x}_{3}}+x{{}_{1}}x{{}_{2}}x{{}_{3}}\]
B) \[f({{x}_{1}},{{x}_{2}}{{x}_{3}})=x{{}_{1}}x{{}_{2}}x{{}_{3}}+x{{}_{1}}x{{}_{2}}x{{}_{3}}\]\[+\,x{{}_{1}}x{{ }_{2}}x{{}_{3}}+{{x}_{1}}{{x}_{2}}{{x}_{3}}\]
C) \[f({{x}_{1}},{{x}_{2}},{{x}_{3}})={{x}_{1}}x{{}_{2}}x{{}_{3}}+x{{}_{1}}{{x}_{2}}x{{}_{3}}\]
D) \[f({{x}_{1}},{{x}_{2}},{{x}_{3}})=x{{}_{1}}{{x}_{2}}{{x}_{3}}+{{x}_{1}}x{{}_{2}}{{x}_{3}}\]
Correct Answer: A
Solution :
In the given table there are four columns. For Ist row \[{{x}_{1}}{{x}_{2}}{{x}_{3}}\] For IInd row \[{{x}_{1}}{{x}_{2}}x{{}_{3}},\] For IIIrd row \[{{x}_{1}}x{{}_{2}}{{x}_{3}}\] For VIth row \[x{{ }_{1}}x{{ }_{2}}x{{ }_{3}}\] Now applying OR to all the combinations obtained, we get the boolean function \[f({{x}_{1}},{{x}_{2}},{{x}_{3}})={{x}_{1}}{{x}_{2}}{{x}_{3}}+{{x}_{1}}{{x}_{2}}x{{}_{3}}\] \[+{{x}_{1}}x{{}_{2}}{{x}_{3}}+x{{}_{1}}x{{}_{2}}x{{}_{3}}\]
You need to login to perform this action.
You will be redirected in
3 sec
