If S is a set with 10 elements and A-x-y-x-y-S-x-y- then the number of elements in A is

Explanation for the correct option.Given the number of elements in S=10and A={(x,y):x,y∈S,x≡y}Then, the number of elements in A is given by:[ ∴A = 10× 9; ...

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Standard XII

Mathematics

One - One function

If S is a set...

Question

If $S$ is a set with $10$ elements and $A = {(x, y) : x, y \in S, x \equiv y}$ , then the number of elements in $A$ is

$100$

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$90$

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$50$

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$45$

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Solution

The correct option is B
$90$

Explanation for the correct option.
Given the number of elements in $S = 10$ and $A = {(x, y) : x, y \in S, x \equiv y}$
Then, the number of elements in $A$ is given by:
$\begin{array}{rcl} ∴ A & = & 10 \times 9 \\ = & 90 \end{array}$ .
Hence, option B is correct.

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If S is a set with 10 elements and A={(x,y):x,y∈S,x≡y}, then the number of elements in A is

The correct option is B 90Explanation for the correct option.Given the number of elements in S=10and A={(x,y):x,y∈S,x≡y}Then, the number of elements in A is given by:∴A=10×9=90.Hence, option B is correct.

If $S$ is a set with $10$ elements and $A = {(x, y) : x, y \in S, x \equiv y}$ , then the number of elements in $A$ is

The correct option is B
$90$

Explanation for the correct option.
Given the number of elements in $S = 10$ and $A = {(x, y) : x, y \in S, x \equiv y}$
Then, the number of elements in $A$ is given by:
$\begin{array}{rcl} ∴ A & = & 10 \times 9 \\ = & 90 \end{array}$ .
Hence, option B is correct.