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Rhea · Accepted Answer

1. The statements given are-
(a)  
(b) 
(c) 
To prove (a)  (b) i.e. 
Let us assume to the contrary that  
Hence, 
But,  which means that if .
This is a contradiction. So, our assumption is wrong and 
To prove (b)  (c) i.e. 
We know that: 
		[Intersection with null set]
			=		[Since, ]
			=		[, by definition]
			= 		[Distributive Law]	
			= 			[U is Universal set]
			= 				[Intersection with Universal set]
Therefore, 
	
To prove (c)  (a) i.e. 
Let,  [Since, ]
		
		
		.
Since, (a) (b) and (b) (c) then it follows from transitivity that (a) (c).
Also, (c) (a) and now (a) (c) then by equivalence (a)(c)
Similarly we can show that (b) (c) and hence (a), (b) and (c) are all logically equivalent.
2. The statements given are-
(a)   
(b) 
(c) 
(c) (b):  If then   
Consider, 
.
(b) (a):  If then , 
Similarly,
Thus,

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