Question

Let n(A) denotes the number of element in set A.if n(A)=P and )B)=q, then how many ordered pairs(a,b) are the with aεA and bεB?

• A. 2pq
• B. p+q
• C. 4qp
• D. pxq

Answer 1

The Correct Option is D

To find the number of ordered pairs \((a, b)\) where \(a \in A\) and \(b \in B\), we need to understand the concept of ordered pairs in set theory.

Given that \(n(A) = p\) and \(n(B) = q\), it implies:

• Set \(A\) contains \(p\) elements.
• Set \(B\) contains \(q\) elements.

An ordered pair \((a, b)\) is formed by taking the first element from set \(A\) and the second element from set \(B\).

Since for each element \(a\) in set \(A\), there are \(q\) choices for element \(b\) in set \(B\), the total number of ordered pairs \((a, b)\) is obtained by multiplying the number of choices for \(a\) by the number of choices for \(b\):

\[ \text{Total ordered pairs} = n(A) \times n(B) = p \times q \]

Thus, the number of ordered pairs \((a, b)\) with \(a \in A\) and \(b \in B\) is \(p \times q\).

The correct answer is: \(p \times q\).