Posted by **heidi** on Friday, April 15, 2011 at 12:22pm.

Fill in the blanks:

For all sets A and B, if A is in the set of B, then A union B in in the set of B.

Proof: Suppose A and B are any sets and A in in the set of B. [we must show that __________] Let x be and element of _______. [we must show that __________] by definition of union, x is an elment of ______ ______ x is an element of _______. In case x is an element of ________, then since A is in the set of B, x is an element of _________. In case x is an element of B, then clearly, x is an element of B. So in either case, x is an element of __________ [as was to be shown]

- discrete math -
**MathMate**, Friday, April 15, 2011 at 3:39pm
Proof: Suppose A and B are any sets and A in in the set of B. [we must show that **A∪B ⊆B**]

Let x be an element of **A∪B**. [we must show that **x∈A or x∈B**] By definition of union, x is an elment of ______ **or** x is an element of _______.

In case x is an element of ________, then since A is in the set of B, x is an element of _________.

In case x is an element of B, then clearly, x is an element of B.

So in either case, x is an element of __________ [as was to be shown]

Hope the above hints are enough for you to complete the proof.

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