I need to show that "A B" (Let this = 'a'), "A B= " (Let this = 'b') and "A B = (universal set)" (Let this = 'c') are equivalent.

a -> b : For A B: Let x A and by definition of subset, x B, so 'a' is true. For (A B = ): In this case, x A and x B implies that 'b' is true, but it is known that x b and this is a contradiction, and A B .

b -> c : For this, I said: By De Morgan's Law, "A B = " is equivalent to (A B )= which is equivalent to A B = which shows that B -> C is true.

c -> a : I am completely stuck on this and need some help.

Any help is appreciated.

Thanks,

Tony