Question

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. a. If ACB and Be C, then ACC b. If xe A and ACB, then x e B c. I​

Answer 1

Answer:

Let A={1,2} and B={1,{1,2},{3}}

2∈{1,2} and {1,2}∈{{3},1,{1,2}}

Now,

∴A∈B

However, 2



∈{{3},1,{1,2}}

(ii) False.

As A⊂B, B∈C

Let A={2},B={0,2}, and C={1,{0,2},3}

However, A



∈C

(iii) True

Let A⊂B and B⊂C.

Let x∈A

⇒x∈B        [∵A⊂B]

⇒x∈C        [∵B⊂C]

∴A⊂C

(iv) False

As, A



⊂B and B



⊂C

Let A={1,2},B={0,6,8}, and C={0,1,2,6,9}

However, A⊂C

(v) False

Let A={3,5,7} and B={3,4,6}

Now, 5∈A and A



⊂B

However, 5



∈B

(vi) True

Let A⊂B and x



∈B.

To show: x



∈A

If possible, suppose x∈A.

Then, x∈B, which is a contradiction as x



∈B

∴x



∈A