230exam1sol

# 230exam1sol - Math 230 E Exam 1 Fri Sep 30 Fall 2011 Drew...

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Math 230 E Fall 2011 Exam 1 — Fri Sep 30 Drew Armstrong There are 4 problems, worth 6 points each. There is 1 bonus point for writing your name. This is a closed book test. Anyone caught cheating will receive a score of zero . 1. [6 points] Let S and T be subsets of the universal set U . (a) Write the statement S 6⊆ T c in terms of logical symbols. S 6⊆ T c = ¬ ( S T c ) = ¬ ( x U, ( x S ) ( x 6∈ T )) (b) Write the statement S T 6 = in terms of logical symbols. x U, ( x S ) ( x T ) (c) Prove that the statements S 6⊆ T c and S T 6 = are logically equivalent. S 6⊆ T c ” = ¬ ( x U, ( x S ) ( x 6∈ T )) = x U, ¬ (( x S ) ( x 6∈ T )) = x U, ¬ ( ¬ ( x S ) ∨ ¬ ( x T )) = x U, ( x S ) ( x T ) = “ S T 6 = 2. [6 points] (a) Prove de Morgan’s law ¬ ( P Q ) = ¬ P ∧ ¬ Q using a truth table. Here is the truth table:

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230exam1sol - Math 230 E Exam 1 Fri Sep 30 Fall 2011 Drew...

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