A) \[(A\times B)\cap (B\times A)=(A\times C)\cap (B\times C)\]
B) \[(A\times B)\cap (B\times A)=(C\times A)\cap (C\times B)\]
C) \[(A\times B)\cup (B\times A)=(A\times B)\cup (B\times C)\]
D) \[(A\times B)\cup (B\times A)=(A\times B)\cup (A\times C)\]
Correct Answer: C
Solution :
Given,\[A=\{1,\text{ }2,\text{ }3\},\text{ }B=\{1,\text{ }2\},\text{ }C=\{2,\text{ }3\}\] \[\therefore \]\[A\times B=\{(1,1),(1,2),(2,1),(2,2),(3,1),\]\[(3,2)\}\] \[B\times A=\{(1,1),(1,2),(1,3),(2,1),(2,2),(2,3)\}\] \[A\times C=\{(1,2),(1,3),(2,2),(2,3),(3,2),(3,3)\}\] \[B\times C=\{(1,1),(1,2),(1,3),(2,1),(2,2),(2,3)\}\] It is clear that \[(A\times B)\cup (B\times A)=(A\times B)\cup (B\times C)\]
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