Question

Question 2 In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

(i) If x∈A and A∈B, then x∈B

(ii) If A⊂B and B∈C, then A∈C

(iii) If A⊂B and B⊂C, then A⊂C

(iv) If A⊄B and B⊄C, then A⊄C

(v) If x∈A and A⊄B, then x∈B

(vi) If A⊂B and x∉B, then x∉A

Class X1 - Maths -Sets Page 26

Answer 1

(i) False
Let A = {4} , B = {{4}, 6, 8}
Then, 4 ∈ A and A ∈ B .
But you observed that 2 ∉B
So, x ∈A , and A ∈B doesn't imply that x ∈B

(ii) False,
Let A = {4}, B = {4,5} and
C = {{4,5},6}
Then, A ⊂B and B ∈C
but A ∉C
so, statement is wrong.

(iii) True,
Let A = {2} , B= {2,3} , and C={2,3,4 }
Here, we observed that ,
A⊂B , B⊂C and also A⊂C
Hence, statement is true.

(iv) False,
Let A = {1,2}
B = {2,3,4 }
and C= {1, 2, 4, 5}
Then, A⊄B, B⊄C but A⊂C
Hence, statement is false.

(v) Flase,
Let A= {2,3} and B {2,4,5,6}
Here, it is clear that 3∈A and
A⊄B but 3∉B.
Hence, this statement is wrong.

(vi) True,
If A⊂B, and x∈A then, must be x∈B.
Let A = {2,3}
B = { 2,3,4,5}
and x = { 1}
Here, it is clear that
A⊂B and x∉A and x∉B.