Question

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}

Answer 1

(i) {a, b} ⊄ {b, c, a} is false. {a, b} ⊂ {b, c, a}

Since, {a, b} is subset of set {b, c,a}.

(ii) {a, e} ⊂ {x: x is a vowel in the English alphabet} is true, because a and e are also vowels of English alphabet.

(iii) {1, 2, 3} ⊂ {1, 3, 5} is false, because element 2 of first set, not occurs in second set.

(iv) {a}, ⊂ [a, b, c} is true, because element a of first set also occurs in second set.

(v) {a} ⊂ [a, b, c} is false, because {a} is a set which is not occurs in second set.

(vi) {.r : x is a natural number less than 6} ⊂ { x : x is a natural number which divides 36} {2,4} ⊂ {1, 2, 3,4, 5, 6, 9, 12, 18, 36}

It is true because 2 and 4 are even natural numbers less than 6 which divides 36.