Consider the following statements. Let A={1,2,3,4}and B={5,7,9}
1.A×B=B×A2.n(A×B)=n(B×A)
Statement-1 is true.
Statement-2 is true
Both are true.
Both are false.
Step 1. Check statement :
Given A={1,2,3,4},B={5,7,9}
A×B={(1,5),(1,7),(1,9),(2,5),(2,7),(2,9),(3,5),(3,7),(3,9),(4,5),(4,7),(4,9)}B×A={(5,1),(5,2),(5,3),(5,4),(7,1),(7,2),(7,3),(7,4),(9,1),(9,2),(9,3),(9,4)}A×B≠B×A
Statement 1 is false.
Step 2. Check Statement 2:
n(A×B)=n(A)×n(B)=4×3=12n(B×A)=n(B)×n(A)=3×4=12n(A×B)=n(B×A)
Statement 2 is true.
Hence, the correct option is B.
Let A and B be two non empty sets such that n(A)=5, n(B)=6 and n(A∩B)=3.
Find (i) n(A×B),
(ii) n(B×A) and
(iii) n(A×B)∩(B×A)