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1. Both Paul and Queenie are happy. (p ^ q) 2. Paul plays the guitar provided that he is happy. (p → r) 3. If Paul is happy and plays the guitar, then Queenie is not happy. ( (p ^ r) → ~q) The pairs of statements (p ∨(q ∧r) and (p ∨q) ∧ (p ∨r)) and (p → q) and p → q) are not logically equivalent based on their truth tables. The converse of "If a quadrilateral is not a rectangle, then it is not a square" is "If it is not a

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Wenceslao Cañete III
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122 views2 pages

Canete Docs

1. Both Paul and Queenie are happy. (p ^ q) 2. Paul plays the guitar provided that he is happy. (p → r) 3. If Paul is happy and plays the guitar, then Queenie is not happy. ( (p ^ r) → ~q) The pairs of statements (p ∨(q ∧r) and (p ∨q) ∧ (p ∨r)) and (p → q) and p → q) are not logically equivalent based on their truth tables. The converse of "If a quadrilateral is not a rectangle, then it is not a square" is "If it is not a

Uploaded by

Wenceslao Cañete III
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Task #3

3.I. Formalize the given statements using the following propositions.


p: Paul is happy.
q: Queenie is happy.
r: Paul plays the guitar.
1. Both Paul and Queenie are happy.
_______p ^q________

2. Paul plays the guitar provided that he is happy.


_______p→q_______

3. If Paul is happy and plays the guitar, then Queenie is not happy.
_______( p^r ) →q____

3.II
Let M: Mark is English and L: Lem is German. Translate the following logic symbols into words.

4. M∨L
Mark is English or Lem is German.

5. M→ L
If Mark is English then Lem is not German.

6. L
Lem is not German.

7. M ∧(∼ L)
Mark is English and Lem is not German.

8. M ∨ (∼ M → L)
Mark is English or If Mark is not English then Lem is German.

A. Construct the truth table for the given compound statements.


1. p ∧(∼ q)
p ∼q p ∧(∼ q)
T F F
T T T
F F F
F T F

2 [ p ∧ ( ∼q ) ] ∨[(∼ p)∨ q]
p q ∼p ∼q p ∧ ( ∼q ) ∼ p ¿∨ q [ p ∧ ( ∼q ) ] ∨[(∼ p)∨ q]
T T F F F T T
T F F T T F T
F T T F F T T
F F T T F T T

B. Determine whether each pair of statements is logically equivalent.


1. p ∨(q ∧r ) and ( p ∨q) ∧(p ∨ r)
p q r q∧r p ∨q p ∨r p ∨ ( q ∧ r ) ( p ∨q ) ∧ ( p ∨r )
T T T T T T T T
T T F F T T F T
T F T T T T T T
T F F F T T F T
F T T F T T F T
F T F F T F F F
F F T F F T F F
F F F F F F F F
Not logically equivalent.

1. ( p → q) and p → q
p q p q ( p → q) p→ q
T T F F T F
T F F T F T
F T T F T F
F F T T T F
Not logically equivalent.

3.III. Write the converse, inverse, and contrapositive of the given statement.
1. If a quadrilateral is not a rectangle, then it is not a square.
Converse : If it is not a square, then a quadrilateral is not a rectangle.
Inverse: If a quadrilateral is a rectangle, then it is a square.
Contrapositive: If it is a square, then a quadrilateral is a rectangle.

2. If yesterday is not Wednesday, then tomorrow is not Friday.


Converse: If tomorrow is not Friday, then yesterday is not Wednesday.
Inverse: If yesterday is Wednesday, then tomorrow is Friday.
Contrapositive: If tomorrow is Friday, then yesterday is Wednesday.

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