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

The Correct Option is A

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.