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Discrete Structure

Assignment 4

This assignment contains part A and part B.

A.   Questions are available in iSpace, please do the questions directly inside iSpace.

B.   Finish the following questions in an e-document and then submit to iSpace.

1.   For sets A, B, C, prove or disprove (with a counterexample) the following: If A ⊆ B, B ⊈ C, then A ⊈C.

2.   Can you conclude that A = B if A, B, and C are sets such that

a)    A⋂C = B⋂C?

b)    （A ∪ C = B ∪ C）∧ (  A ∩ C = B ∩ C)?

3. Show that if A and B are sets, then (B - A) ∪ (C - A) = (B ∪ C) – A using laws.

4. Prove the De Morgan law by showing that if A and B are sets, then A ∪ B = A ∩ B by showing each side is a subset of the other side