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3 years ago

DISCRETE MATHEMATIC

Mathematics

1 answer:

Jet001 [13]3 years ago

6 0

Answer:

The conclusion "T" logically follows from the premises given and the argument is valid

Step-by-step explanation:

Let us use notations to represent the steps

P: I take a bus

Q: I take the subway

R: I will be late for my appointment

S: I take a taxi

T: I will be broke

The given statement in symbolic form can be written as,

(P V Q) → R

S → (¬R ∧ T)

(¬Q ∧ ¬P) → S

¬R

___________________

∴ T

PROOF:

1. (¬Q ∧ ¬P) → S Premise

2. S → (¬R ∧ T) Premise

3. (¬Q ∧ ¬P) → (¬R ∧ T) (1), (2), Chain Rule

4. ¬(P ∨ Q) → (¬R ∧ T) (3), DeMorgan's law

5. (P ∨ Q) → R Premise

6. ¬R Premise

7. ¬(P ∨ Q) (5), (6), Modus Tollen's rule

8. ¬R ∧ T (4), (7), Modus Ponen's rule

9. T (8), Rule of Conjunction

Therefore the conclusion "T" logically follows from the given premises and the argument is valid.

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-----------------------------

Normal Probability Distribution

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