CS301KFall 2013J. Schrum

Name:EID:

Date:

Midterm 1 for CS301K Fall 2013

A. For each item below, circle either TRUE, FALSE, or NOT A PROPOSITION.(2 points each)

1. Some dogs bark.

TRUE FALSE NOT A PROPOSITION

2. Do well on this test!

TRUE FALSE NOT A PROPOSITION

3. ∃x ∈ Z∀y ∈ Z[x + y = y]

TRUE FALSE NOT A PROPOSITION

4. ∀x ∈ Z∃y ∈ Z[x + y = y]

TRUE FALSE NOT A PROPOSITION

B. Analyze the logical forms of the following statements without using anypredicates. Define your propositional variables. (4 points each)

1. Robert will go to jail if he robs the bank and gets caught.

2. Ken will eat the apple if and only if it is not rotten.

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CS301KFall 2013J. Schrum

Name:EID:

Date:

C. Analyze the logical form of the following statement assuming the universefor all variables is “people” and using only the following predicate:P (x, y) =“x is a parent of y” (4 points)

The parents of one of Eric’s parents are named Alice and John.

D. Write a linear proof of the following equivalence. (10 points)A ∧ (B → ¬(C ∧ ¬A)) ≡ A.

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CS301KFall 2013J. Schrum

Name:EID:

Date:

E. Use rules of inference and logical identities to prove the following argument.(10 points)

P ∨QP → QQ→ R

∴ R

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CS301KFall 2013J. Schrum

Name:EID:

Date:

F. Suppose m, n ∈ Z. Prove (mn even) → (m even ∨ n even). (10 points)

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CS301KFall 2013J. Schrum

Name:EID:

Date:

Scratch Paper

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