Showing posts with label Examine whether the following statements are true or false. Show all posts
Showing posts with label Examine whether the following statements are true or false. Show all posts

Tuesday, 8 April 2014

Examine whether the following statements are true or false

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
(i) False.
All element of {a, b} lies in set {b, c, a}. So {a, b} ⊂ {b, c, a}
Hence given statement is false.
(ii) True.
‘a’ and ‘e’ both are vowels of the English alphabet.
So that , {a, e} ⊂ {x: x is a vowel in the English alphabet}.
Hence given statement is true.
(iii) False.
‘2’ lies in set {1, 2, 3} but don’t lies in set {1, 3, 5}
So that, {1, 2, 3} ⊄ {1, 3, 5}.
Hence, given statement is false.
(iv) True.
All elements of set {a} are also an element of set {a, b, c}.
So that, {a} ⊂ {a. b, c}
Hence, given statement is true.
(v) False.
{a} is not an element of set {a, b, c}.
So that correct statement will a ∈ {a. b, c}
Hence, given statement is False.
(vi) True.
Even natural numbers less than 6 are 2 and 4.
Natural numbers which are divided by 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.
2 and 4 both lies in set { 1, 2, 3, 4, 6, 9, 12, 18, 36}.
So that {x: x is an even natural number less than 6} ⊂ {x: x is a natural number which divides 36}
Hence, given statement is true.