Question 26c2d

Sep 27, 2016

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Explanation:

Ans. to Q(1) : To verify whether a set $A$ is a subset of another

set $B$, we have to check that, each & every element of the set

$A$ is also an element of the set $B$.

Here, the set $A$ has two elements, namely, 1 & 2, and we see

that they are also the elements of the set B.

Accordingly, $A \subset B$.

Ans. to Q(2) :

The complement of $B$ (in $\mathbb{N}$), denoted by $B '$ is the set of

all those elements in NN which are not in $B$.

Hence, $B ' = \left\{3 , 4 , 5 , \ldots \ldots \ldots \ldots\right\}$.

We may write, $B ' = \mathbb{N} - \left\{1 , 2\right\}$.

Ans. to Q(3) :

Indeed, $A = B \iff A \subset B , \mathmr{and} , B \subset A$.

In fact, this is the Defn. of Equality of Sets.