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.

Answer: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 = BThus, If A ⊆ B, then A ⊂ B.Option a is true.(b) If A ⊂ B⇒ A is the subset of BThat is, all elements of A are also the element of B,But we can not say A = BThus, 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 ⊂ BOption d is true.(e) If A ⊂ B,Then we can not say that,A = B or A ≠ BThus, option e is not correct.