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ra1l [238]
3 years ago
9

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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