Question

if set A has p elements, B has q elements, then the number of elements in A×B is. (a) p+q (b) p+q+1 (c) pq (d) p^2​

Answer 1

Answer:

PxQ=pq

I hope it is useful

Answer 2

Concept:

The number of order pairs in cross section of two sets is given by the product of numbers of elements of each sets.

Given:

Set A has $p$ elements and Set B has $q$ elements.

Find:

The number of elements in $A\times B$ when the Sets A and B are like above mentioned.

Solution:

Set A contains $p$ number of elements

where Set B contains $q$ number of elements

Thus the number of elements in $A\times B=p\times q=pq$

For example:

Let assume the set $A=\{1,2,3\},B=\{1,2\}$

Then number of elemets in $A=3,B=2$

Now, $A\times B=\{(1,1),(1,2),(2,1),(2,2),(3,1),(3,2)\}$

So the number of elements in $A\times B=6(=2\times 3)$

Hence the number of elements in $\mathbf{A\times B=pq}$.

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