Question

OA + OC = AC STATE WHETHER TRUE WITH FALSE ALSO GIVE REASON IN SUPPORT OF YOUR ANSWER​

Answer 1

Answer:

(i) False

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