Answer to Question #182999 in Discrete Mathematics for Maricel

Question

A. Show whether or not p → q ≡ (p ^ q) v (𝒑̅ ^ 𝒒̅) 

B.Let P(x) denote the statement

1

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x2+1>1. If its domain are all real numbers,

what is the truth value of the following quantified statement? (5 pts each)

1. ∃xP(x)

2. ∀xP(x)

C. What rule of inference is used in each of the following arguments? Show

solution. (5 pts each)

1. If it will rain today, then the classes are suspended. The classes are not suspended today. Therefore, it did not rain today.

2. If you read your module today, then you will not play ML today. If you

cannot play ML today, you can play ML tomorrow. Therefore, you read

your module today, then you will play ML tomorrow.

Answer 1

A. Show whether or not p → q ≡ (p ^ q) v (¬p ^ ¬q)

Answer: False

B.Let P(x) denote the statement x²+1>1. If its domain are all real numbers, what is the truth value of the following quantified statement? (5 pts each)

1. ∃xP(x)

Answer: true (for example x = -9.9)

2. ∀xP(x)

Answer: false (if x = 0, then P(x) breaks)

C. What rule of inference is used in each of the following arguments? Show solution. (5 pts each)

1. If it will rain today, then the classes are suspended. The classes are not suspended today. Therefore, it did not rain today.

Answer:

p – it is rain today

q – the classes are suspended today

p→q (if it will rain today, then the classes are suspended)

¬q (the classes are not suspended today)

modus tollens: ¬q, p→q ├ ¬p (it did not rain today)

2. If you read your module today, then you will not play ML today. If you cannot play ML today, you can play ML tomorrow. Therefore, you read your module today, then you will play ML tomorrow.

Answer:

p – you read your module today

q – you don’t play ML today

r – you play ML tomorrow

p→q (if you read your module today, then you will not play ML today)

q→r (if you cannot play ML today, you can play ML tomorrow)

hypothetical syllogism : p→q, q→r ├ p→r (if you read your module today, then you will play ML tomorrow)