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.

(e)

if a ⊂ b, then a ≠ b.

If A ⊆ B, then A ⊂ B.

If A = B, then A ⊆ B.

If A = B, then A ⊂ B.

Step-by-step explanation:

In set theory '⊂' is the symbol of proper subset and '⊆' is the symbol of subset of a set.

In option (a),

If A ⊆ B

⇒ A ⊂ B or A = B

Thus, If A ⊆ B, then A ⊂ B.

Option a is true.

(b) If A ⊂ B

⇒ A is the subset of B

That is, all elements of A are also the element of B,

But we can not say A = B

Thus, option b is not true.

(c) If A = B

⇒ A ⊂ B and A ⊃ B or A ⊆ B and B ⊆ A ( Because every set is the subset of itself )

⇒  A ⊆ B.

Option c is true.

(d) If A = B,

⇒ A ⊂ B

Option d is true.

(e) If A ⊂ B,

Then we can not say that,

A = B or A ≠ B

Thus, option e is not correct.

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.

i = 2 / - 5

step-by-step explanation:

evaluation of ( 2 - 4 ) ( p + q ) when p = 2 and q = 5 i, by putting values of p and q,