Examine whether the following statements are true or false

Tuesday, 8 April 2014
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.

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