Examine whether the following statements are true or false:

(i) {a, b} ⊄ {b, c, a}

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

(iii) {1, 2, 3} ⊂ {1, 3, 5}

(iv) {a} ⊂ {a, b, c}

(v) {a} ∈ {a, b, c}

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

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

Now, we can observe that every element of A is an element of B.

Thus, A⊂ B

∴ The statement is false.

(ii) Let us assume that A = {a, e} and

B = {x: x is a vowel in the English alphabets}

={a, e, i, o, u}

Now, we can observe that every element of A is an element of B.

Thus, A⊂ B

∴ The statement is true.

(iii) Let us assume that A = {1, 2, 3} and B = {1, 3, 5},

Now, we can observe that 2 belongs to A but 2 does not belongs to B.

Thus, A B

∴ The statement is false.

(iv) Let us assume that A = {a} and B = {b, c, a}

Now, we can observe that every element of A is an element of B.

Thus, A⊂ B

∴ The statement is true.

(v) Let us assume that A = {a} and B = {b, c, a}

Now, we can observe that every element of A is an element of B.

Thus, A⊂ B

∴ The statement is false.

(vi) Let us assume that A = {x:x is an even natural number less than 6}

= {2, 4}

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

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

Now, we can observe that every element of A is an element of B.

Thus, A⊂ B

∴ The statement is true.