Which of the following statements are always true for any two sets A and B? (a)

Question

Which of the following statements are always true for any two sets A and B?

(a)

If A B, then A B.

(b)

If A B, then A B.

(c)

If A = B, then A B.

(d)

If A = B, then A B.

3.2.4

Let X = {a, b, c, d}. What is{ A: A P(X) and |A| = 2 }?

3.6.4

Express each set in roster notation. Express the elements as strings, not n-tuples.

(a)

A2, where A = {+, -}.

(b)

Which of the following statements are always true for any two sets A and B?

(c)

(a)

If A B, then A B.

(b)

If A B, then A B.

(c)

If A = B, then A B.

(d)

If A = B, then A B.

3.2.4

Let X = {a, b, c, d}. What is{ A: A P(X) and |A| = 2 }?

3.6.4

Express each set in roster notation. Express the elements as strings, not n-tuples.

(a)

A2, where A = {+, -}.

(b)

A3, where A = {0, 1}.

A3, where A = {0, 1}.

Explanation / Answer

(1)

(a)

If A B, then A B.

It means that if A is subset of B ....then A is proper subset of B

It is TRUE

(b)

If A B, then A B

It means that if A is proper subset of B ....then A is subset of B

so, all element of A will never be same in B in case of proper subset

while in subset ...there can be all element of A will be same in B

It is FALSE

(c)

If A = B, then A B.

If all elements of A and B are same

because in subset it is possible to have same element on both A and B

then A is subset of B

It is TRUE

(d)

If A = B, then A B

If all elements of A and B are same

then A is proper subset of B

which is not true

because all elements of both A and B must be same

so,

It is FALSE

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