Question

11. Let A = {1, 2, 5, 6), 7). Which of the following statements are not true and why? (1) {1, 2} E A (ii) {1, 2, 7) CA (iii) {5. 6) CA (iv) {φ} C A ​

Answer 1

Answer:

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 Read more on Sarthaks.com - https://www.sarthaks.com/5199/let-a-1-2-3-4-5-which-of-the-following-statements-are-incorrect-and-why

Step-by-step explanation:

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 statement {{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 Φ ∈ A is incorrect because Φ is not an element of A. (x) The statement Φ ⊂ A is correct because Φ is a subset of every set. (xi) The statement {Φ} ⊂ A is incorrect because Φ∈ {Φ}; however, Φ ∈ A. Read more on Sarthaks.com - https://www.sarthaks.com/5199/let-a-1-2-3-4-5-which-of-the-following-statements-are-incorrect-and-why

Answer 2

Step-by-step explanation:

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