paganinio

Hi, Could you help me with these problems please??

1. Use Venn diagrams or membership table to demonstrates that:

A U (B ∩ C)= (A U B) ∩ (A U C) is a true equation for any sets A, B, and C. If you use Venn diagrams , show the three circles overlapping and include a legend pointing out which set is represented by witch shaded regions.

2. Find the best conclusion for this Lewis Carroll problem . The "best" conclusion is one which uses all of the given information.

A. No one who is going to a party ever fails to brush his hair.

B. No one looks fascinating , if he is untidy.

C. Opium -eaters have no self-command.

D.Everyone who has brushed his hair looks fascinating.

E.No one wears white kid gloves unless he is going to a party.

F. A person is always untidy if he/she has no self -command.

Assign letters to the statements , write the premises using logic symbols , write a valid argument which leads to the best conclusion , then write the conclusion in words.

3. Prove this statement : For all X ε { 2,4,6,8,12,10}, 3x +12 is an even number.

Please help !!! Thanks(Headbang)