Given the following sets: W={w | w is a whole number}, A={a | a=2w+2, w∈W} A⊆W, B={b | b=2w+1, w∈W} B⊆W Determine the following: A∩B Explain the answer.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

A is the set of even numbers excluding zero.

Explanation: w=0 => 2w+2=2, w=1 =>2w+2=4, w=3 =>2w+2=6, etc.

B is the set of odd numbers.

Explanation: w=0=>2w+1=1, w=1 =>2w+1=3, w=2=>2w+1=5, etc.

`AnnB=O/`

Explanation: The symbol between A and B means we are looking for the intersection between the two sets. In other words we are looking at all the elements that belong to both A and B. Since A is the set of even numbers, and B is the set of odd numbers, their intersection is empty. An O with a line crossing it symbolizes an empty set.

 

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