How do you prove these theorems about sets?

Question

-- (A U B) is a subset of (A U B U C)

-- (A ∩ B ∩ C) is a subset of (A ∩ B)

-- (A - B) - C is a subset of (A-C)

-- (B - A) U (C - A) - (B U C) - A

-- (A is a subset of B) ≡ [(A ∩ B) = A]

-- A XOR B = (A U B) - (A ∩ B)

-- A XOR B = (A - B) U (B - A)

Answer 1

In general to prove that a set A is a subset of B, suppose x is in A and show that x must also be in B. So use the definitions of the set operators and the proof should be straight forward.