Question

Examine whether the following statements are true or false :

(i) {a, b} $\subset ̸$ {b, c, a}

(ii) {a, e} $\subset$ {x: x is a vowel in the English alphabet}

(iii) {1, 2, 3} $\subset$ {1, 3, 5}

(iv) {a} $\subset$ {a, b, c}

(v) {a} $\in$ {a, b, c}

(vi) {x : x is an even natural number less than 6} $\subset$ {x : x is a natural number which divides 36}

Answer 1

(i) Let A = {a, b} and B = {b, c, a}

Then every element of A is an element of B.

$\therefore$ $A\subset B$

Hence the statement is false.

(ii) Let A = {a, e} and B = {x : x is a vowel in the English alphabet}

$\therefore$ B = {a, e, i, o, u}

$\therefore$ Then every element of A is an element of B

$\therefore$ $A\subset B$

(iii) Let A = {1, 2, 3} and {1, 3, 5}.

Here $2\in A$ but $2\notin B.$

$\therefore$ $A\subset ̸B$

Hence the statement is false.

(iv) Let A = {a} and B = {a, b, c}.

Then every element of A is an element of B.

$\therefore$ $A\subset B$

Hence the statement is true.

(v) Let A = {a} and B = {a, b, c}.

Here the statement is false because {a} $\notin B.$ Note that A is subset of B and not an element of B.

(vi) Let A = {x : x is an even natural number less then 6}

A = {2, 4} and

B = {x : x is a natural number which divides 36}

B = {1, 2, 3, 4, 6, 9, 12, 18, 36}

Here every element of A is an element of B.

$\therefore$ $A\subset B$ Hence the statement is true.