Question

Let A = {1, 2, {3, 4}, 5}. Which of the following statements are incorrect and why?

(i) {3, 4} ⊂ A
(ii) {3, 4} ∈ A
(iii) {{3, 4}} ⊂ A
(iv) 1 ∈ A
(v) 1 ⊂ A
(vi) {1, 2, 5} ⊂ A
(vii) {1, 2, 5} ∈ A
(viii) {1, 2, 3} ⊂ A
(ix) ϕ ∈ A
(x) ϕ ⊂ A
(xi) {ϕ } ⊂ A

Answer 1

Answer:

(i) Let us assume that A = {a, b} and B = {b, c, a}

Now, we can observe that every element of A is an element of B.

Thus, A⊂ B

∴ The statement is false.

(ii) Let us assume that A = {a, e} and

B = {x: x is a vowel in the English alphabets}

={a, e, i, o, u}

Now, we can observe that every element of A is an element of B.

Thus, A⊂ B

∴ The statement is true.

(iii) Let us assume that A = {1, 2, 3} and B = {1, 3, 5},

Now, we can observe that 2 belongs to A but 2 does not belongs to B.

Thus, A B

∴ The statement is false.

(iv) Let us assume that A = {a} and B = {b, c, a}

Now, we can observe that every element of A is an element of B.

Thus, A⊂ B

∴ The statement is true.

(v) Let us assume that A = {a} and B = {b, c, a}

Now, we can observe that every element of A is an element of B.

Thus, A⊂ B

∴ The statement is false.

(vi) Let us assume that A = {x:x is an even natural number less than 6}

= {2, 4}

and B = {x:x is a natural number which divide 36}

= {1, 2, 3, 4, 6, 9, 12, 18, 36}

Now, we can observe that every element of A is an element of B.

Thus, A⊂ B

∴ The statement is true.

JAI SHREE KRISHNA

Answer 2

1,5,8,9,11 are incorrect

because

1- it is not a subset of A

5-1 is also not a subset of A

8- the digit 3 is not seperately kept in set A

9-pi does not belongs to set A

and 11 is also a same explanation