NCERT Solutions
Class 11 Maths
Sets
Ex.1.3 Q.3
Let A = {1, 2, {3, 4}, 5}. Which of the following statements are incorrect and why?
(1) {3, 4} ⊂ A
(2) {3, 4} ∈ A
(3) {{3, 4}} ⊂ A
(4) 1 ∈ A
(5) 1 ⊂ A
(6) {1, 2, 5} ⊂ A
(7) {1, 2, 5} ∈ A
(8) {1, 2, 3} ⊂ A
(9) φ ∈ A
(10) φ ⊂ A
(11) {φ} ⊂ A
Given, A = {1, 2, {3, 4}, 5}
(1) The statement {3, 4} ⊂ A is incorrect because 3 ∈ {3, 4}; however, 3 ∉ A.
(2) The statement {3, 4} ∈A is correct because {3, 4} is an element of A.
(3) The statement {{3, 4}} ⊂ A is correct because {3, 4} ∈ {{3, 4}} and {3, 4} ∈ A.
(4) The statement 1∈A is correct because 1 is an element of A.
(5) The statement 1⊂ A is incorrect because an element of a set can never be a subset of itself.
(6) The statement {1, 2, 5} ⊂ A is correct because each element of {1, 2, 5} is also an element of A.
(7) The statement {1, 2, 5} ∈ A is incorrect because {1, 2, 5} is not an element of A.
(8) The statement {1, 2, 3} ⊂ A is incorrect because 3 ∈ {1, 2, 3}; however, 3 ∉ A.
(9) The statement φ ∈ A is incorrect because φ is not an element of A.
(10) The statement φ ⊂ A is correct because φ is a subset of every set.
(11) The statement {φ} ⊂ A is incorrect because φ ∈ {φ}; however, φ ∈ A.