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 × B is 7 then p² + q² = ________.

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 $p^{2} + q^{2} =$ ________.

Smart Achievers · Accepted Answer

(1)

We have, $p$

$n (A \times B) = p \times q \Rightarrow 7 = p q$

$\Rightarrow Either p = 1, q = 7 or q = 1, p = 7$

$∴$ $p^{2} + q^{2} = 1^{2} + 7^{2} = 50$

Solution

Q.
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 $p^{2} + q^{2} =$ ________.

1 50

2 42

3 51

4 49

Ans.
(1)

We have, $n (A) = p, n (B) = q$

$n (A \times B) = p \times q \Rightarrow 7 = p q$

$\Rightarrow Either p = 1, q = 7 or q = 1, p = 7$

$∴$ $p^{2} + q^{2} = 1^{2} + 7^{2} = 50$

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