State whether the following statements are true or false:(i) 1 ∈ {

1.	State whether the following statements are true or false:(i) 1 ∈ { 1,2,3}(ii) a ⊂ {b,c,a}(iii) {a} ∈ {a,b,c}(iv) {a, b} = {a, a, b, b, a}(v) The set {x: x + 8 = 8} is the null set.
Answer» (i) True Since, 1 belongs to the given set {1, 2, 3} as it is present in it. (ii) False Here, a is an element and not a subset of a set {b, c, a} (iii) False Here, {a} is a subset of set {b, c, a} and not an element. (iv) True Since, we do not have repeat same elements in a given set. (v) False Given as, x + 8 = 8 i.e. x = 0 Therefore, the given set is a single ton set {0}. Here, it is not a null set.

State whether the following statements are true or false:(i) 1 ∈ { 1,2,3}(ii) a ⊂ {b,c,a}(iii) {a} ∈ {a,b,c}(iv) {a, b} = {a, a, b, b, a}(v) The set {x: x + 8 = 8} is the null set.

Answer»

(i) True

Since, 1 belongs to the given set {1, 2, 3} as it is present in it.

(ii) False

Here, a is an element and not a subset of a set {b, c, a}

(iii) False

Here, {a} is a subset of set {b, c, a} and not an element.

(iv) True

Since, we do not have repeat same elements in a given set.

(v) False

Given as, x + 8 = 8

i.e. x = 0

Therefore, the given set is a single ton set {0}. Here, it is not a null set.