E ACTIVITY

1.5.3: Expand then reduce the proposition.

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Simplify (p(mp)) to pm

3. Select ba from (ab)(ba) belowShow me how

(p(mp))

CANCEL LAW

Laws

Distributive

(ab)(ac)

a(bc)

(ab)(ac)

a(bc)

Commutative

ab

ba

ab

ba

De Morgan's

(ab)

ab

(ab)

ab

Conditional

ab

ab

ab

(ab)(ba)

Complement

aa

T

aa

F

T

F

F

T

Identity

aT

a

aF

a

Double negation

a

a

1

2

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1

2

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Additional exercises

Exercise 1.5.1: Label the steps in a proof of logical equivalence.

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Below are several proofs showing that two logical expressions are logically equivalent. Label the steps in each proof with the law used to obtain each proposition from the previous proposition. The first line in the proof does not have a label.

(a)

(p q) (q p)

(p q) (q p)

(q p) (q p)

q (p p)

q (p p)

q F

q

(b)

(p q) (p q)

(p q) (p q)

(p q) (p q)

(p q) (p q)

p (q q)

p T

p

(c)

r (r p)

r (r p)

r (r p)

(r r) p

r p