Question

Suppose that the number of elements in set A is p, the number of elements in set B is q and the number of elements in $A \times B$ is 7 then $p^2 + q^2 =$

• A. 50
• B. 42
• C. 51
• D. 49

Answer 1

Answer: (A)

50

Answer 2

The number of elements in the Cartesian product $A \times B$ is given by the product of the number of elements in set A and the number of elements in set B. So, we have:
$|\vec{A} \times \vec{B}| = |\vec{A}| \cdot |\vec{B}| = 7$
Since$|\vec{A} \times \vec{B}| = 7$, we know that $p \cdot q = 7$
To find the value of $p^2 + q^2$, we need to find the possible values of p and q that satisfy $p \cdot q = 7$.
The possible pairs of (p, q) that satisfy $p \cdot q = 7$ are (1, 7) and (7, 1).
For both pairs, $p^2 + q^2 = 1^2 + 7^2 = 1 + 49 = 50.$
Therefore, $p^2 + q^2 = 50.$
The correct option is (A) 50.