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)

Since all the elements of { a,b } are contained in { b,c,a }, so, the given statement { a,b }⊄{ b,c,a } is false.

(ii)

Since a and e are the vowels of the English alphabet, so, the given statement { a,e }⊂{ x:x is a vowel in the English alphabet } is true.

(iii)

Since all the elements of { 1,2,3 } are not contained in { 1,3,5 }, so, the given statement { 1,2,3 }⊂{ 1,3,5 } is false.

(iv)

Since a is contained in { a,b,c }, so, the given statement { a }⊂{ a,b,c } is true.

(v)

Since the elements of the set { a,b,c } are a,b,c, so, the element { a } does not belong to { a,b,c }, so, the given statement { a }∈( a,b,c ) is false.

(vi)

The even natural numbers less than 6 is 2 and 4.

The natural numbers which divides 36 are 1,2,3,4,6,9,12,18,36.

Since { 2,4 } are contained in { 1,2,3,4,6,9,12,18,36 }, so, the given statement { x:x is an even natural number less than 6 }⊂{ x:x is a natural number which divides 36 } is true.