Practice Problems-Truth Tables PDF

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Practice Problems: Truth Tables Put the following arguments in their argument form by assigning letters (like P and Q) to the simple sentences and using the connective symbols to connect them. Then use a truth table to determine whether or not the following arguments are valid. a) 1) 2) 3) 4)

Either all birds sing, or nature has failed us. Either nature has not failed us, or we are doomed to die. We are not doomed to die. All birds sing.

b) 1) All dogs go to heaven. 2) Either all dogs go to heaven, or all dogs go to heck.

c) 1) 2) 3) 4)

Either I’m not well, or I’m drunk. Either I’m seasick, or I’m drunk. I’m well, or I’m not seasick. I’m drunk.

d) 1) It is not the case that I like cake and pie 2) I like cake 3) I don’t like pie For the following arguments, create a truth table to determine if they are valid or invalid: e) P → ~Q R ↔ P∧Q Q∨R

Q∧R f) (X→Y) → Z ~Z ~Y g) W→U ~W → V U∨V h) P ∨ (Q∧S) S∨Q S ∨ ~P S

Answers questions (a) to (d) a) 5) 6) 7) 8) S T T T T F F F F

SvN ~NvD ~D S N T T F F T T F F

D T F T F T F T F

~N F F T T F F T T

SvN T T T T T T F F

~NvS T T T T F F T T

~D T F T F T F T F

S T T T T F F F F

There is no row of the truth table in which all the premises are true and the conclusion is false. Therefore the argument is valid. b) 1) P 2) P v Q P T T F F

Q T F T F

PvQ T T T F

There is no row of the truth table in which all the premises are true and the conclusion is false. Therefore the argument is valid.

c) 5) 6) 7) 8) W T T T T F F F F

~W v D. S v D. W v ~S. D S T T F F T T F F

D T F T F T F T F

~W F F F F T T T T

SvD T T T F T T T F

W v ~S T T T T F F T T

~WvD T F T F T T T T

D T F T F T F T F

There is no row of the truth table in which all the premises are true and the conclusion is false. Therefore the argument is valid. d) 1) ~(C&P) 2) C 3) ~P C T T F F

P T F T F

~ (C & P) F T T T

C T T F F

~P F T F T

This argument is valid because there is no line of the truth table in which the premises are both true and the conclusion is false....