Im really struggling to understand how to conceptually go ab

I\'m really struggling to understand how to conceptually go about these questions. Right now I\'ve answered True, False, False, True, but I\'m very unsure. Could someone help me out in also telling me how I should approach problems like these?

1. You will need the following definitions for this question: (i) If A is a subset of B and A B, we say that A is a proper subset of B. This is notated as ACB (ii) Two sets are equal if they contain the same elements. That is, A B if var (r e A e B). B A c B c A r equivalently, A if and B Let U be the collection of all finite subsets, including 0, of the set N. Determine if each statement below is true or false. You do not need to justify your answer; just write the word True or False. (a) VX3Y, X C Y (b) VY3X, X CY (c) 3YvX, X C Y (d) 3xvY, X c Y

Solution

a. For all x there exist y

For Every element of x there is one element in Y

so x is proper subset of y

True.

2.for all y there exist x

for every element of y there exist x

That means y is proper subset of x

False

C.there exist y for all x

There exist one element for every element in x

So y is proper subset of x

False

D.there exist x for all y

There exist one element in x for every element in y

So x is proper subset of y

True