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Byju's Answer

Standard IX

Mathematics

Subset of a Set

If A is a pro...

Question

If $A$ is a proper subset of $B$ , then $n (A)$ $n (B)$ .

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Solution

The correct option is A $<$
If $A$ is an arbitrary subset of $B$ , then $n (A) \leq n (B)$ .
But when $A$ is a proper subset of $B$ , the number of elements in $A$ is strictly less than that in $B$
i.e. $n (A) < n (B)$

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Let A={all quadrilaterals}, B={all rectangles}, C={all squares} and D={all rhombuses} in a plane. State, giving reasons, whether the following statements are true or false:

i) B is proper subset of C is proper subset of A

ii) C is proper subset of B is proper subset of A

iii) C is proper subset of D is proper subset of A

iv) D is proper subset of C and is proper subset of A

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If A is a proper subset of B, then n(A)n(B).

The correct option is A <If A is an arbitrary subset of B, then n(A)≤n(B). But when A is a proper subset of B, the number of elements in A is strictly less than that in B i.e.n(A)<n(B)

If $A$ is a proper subset of $B$ , then $n (A)$ $n (B)$ .

The correct option is A $<$
If $A$ is an arbitrary subset of $B$ , then $n (A) \leq n (B)$ .
But when $A$ is a proper subset of $B$ , the number of elements in $A$ is strictly less than that in $B$
i.e. $n (A) < n (B)$