Discrete Mathematics Answers

Consider

Premises: If there was a cricket match, then traveling was difficult.

If they arrived on time, then traveling was not difficult.

They arrived on time.

Conclusion: There was no cricket match.

Determine whether the conclusion follows logically from the premises. Explain by

representing the statements symbolically and using rules of inference

Consider the argument:

"Mary is a diabetic.

If Mary is a diabetic, then Frank is a television watcher.

If Frank is a television watcher, then Mark is not unhappy.

Either James is a watermelon, or Mark is happy."

Formalize this argument, and make a conclusion about James.

a) Show that the following logical equivalences hold for the Peirce arrow↓, where

P ↓Q = ~ (P ∨ Q).

P ∨ Q = (P ↓ Q) ↓ (P ↓ Q)

P ∧ Q= (P ↓ P) ↓ (Q ↓ Q)

b) Show that for the Shuffer stroke |

P ∧ Q = (P | Q) | (P | Q)

c) Use the result from (b) and example 2.4.7 from book to write P ∧ (∼Q ∨ R) using only

Shuffer strokes

Consider the argument:

"Mary is a diabetic.

If Mary is a diabetic, then Frank is a television watcher.

If Frank is a television watcher, then Mark is not unhappy.

Either James is a watermelon, or Mark is happy."

Formalize this argument, and make a conclusion about James.

Formalize the following argument, then determine the result using logical Inferences

Either Derek works or Avery does not work.

If it is not true that both Avery works and Brandon does not work, then clearly Celina does not

work. However, Derek does not work."

Does Celina work?

I. Determine if each statement is a proposition. If so, also determine its truth value.

1. Read and follow instructions.
2. Ok I answered the assignment.
3. 2+3=5
4. Let x be 5, x+y=10.
5. DLSU-CCS is in Quezon City.

V. Determine whether each pair of propositions are logically equivalent or not. Use Logical Equivalence Rules.

1. ¬(p∨(¬p∧q)) and ¬p∧¬q
2. ¬(p↔q) and p↔¬q
3. p↔(q∧r) and (p↔q)∧(p↔r)
4. ¬(p↔q) and p⊕q

IV. Use Logical Equivalence Rules to simplify the following. Construct the truth tables for each of the compound propositions and its simplified expression.

1. ¬b∧(a→b)∧a
2. (a→b)↔(¬a∨b)
3. ((p→q)→r)∧(¬q↔(p∧¬q))
4. ¬a∧(b⊕c)∧(¬b∨c)

III. State the converse, inverse, and contrapositive of each of the given statements.

1. If it snows tonight, I will stay home.
2. I go to the beach whenever it is a sunny summer day.
3. A positive integer is prime only if it has no divisors other than 1 and itself.

DLSU-CCS is in Quezon City.