Question

Let A = {1, {2}, {3,4}, 5}. Is it incorrect statement? Recitify:1<A​

Answer 1

Solution :

Clearly, A contains four elements, namely 1,{2},{3,4}and5

(i) 2∈A is incorrect. The correct statement would be {2}∈A.

(ii) {2}⊂A is incorrect. The correct statement is {{2}}⊂A.

(iii) Clearly, 2l∈A and therefore , {1,2}⊂A is correct. THe correct statement would be {1,{2},}⊂A.

(iv) Clearly, {3,4} is an element of A. So, {3,4},⊂A is incorrect and {{3,4}}⊂A is correct.

(v) Since 1 and 5 are both elements of A, so {1,5}⊂A is correct.

(vi) Since ϕl∈A, so {ϕ}⊂A is incorrect while ϕ⊂A is correct.

(vii) Since 1∈A, so 1⊂A in incorrect and therefore , {1}⊂A is correct.

(viii) Since 2l∈Aand3l∈A , so {1,2,3,4}⊂A is incorrect. The correct statement would be {1,{2},{3,4}}⊂A.