Question

. If A = {1, {1}, 2, 3, {2,3}, 4, 5). Make the following statements true by putting appropriate symbols C, ¢, E, & in the blanks. i) {1, 3}___A ii) 1___ А iii) {1} A iv) {1,
2, 3)___ A v) {4, 5} ___A vi) 6___ А​

Answer 1

Answer:

It is given that A=(1,2,(3,4),5)

(i)The statement (3,4)⊂A is incorrect because 3∈(3,4); however, 3∈

/

A.

(ii) The statement (3,4)∈A is correct because (3,4) is an element of A.

(iii) The satement ((3,4))⊂A is correct because (3,4)∈((3,4)) and (3,4)∈A.

(iv) The statement 1∈A is correct because 1 is an element of A.

(v) The statement 1⊂A is incorrect because an element of a set can never be a subset of itself.

(vi) The statement (1,2,5)⊂A is correct because each element of (1,2,5) is also an element of A.

(vii) The statement (1,2,5)∈A is incorrect because (1,2,5) is not an element of A.

(viii) The statement (1,2,3)⊂A is incorrect because 3∈(1,2,3); however, 3∈

/

A.

(ix) The statement



◯∈A is incorrect because



◯ is not an element of A.

(x) The statement



◯⊂A is correct because



◯ is a subset of every set.

(xi) The statement (



◯)⊂A is incorrect because



◯ is a subset of A and it is not an element of A.