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Question 1. Using the truth table, determine whether the following two propositi

ID: 3753121 • Letter: Q

Question

Question 1. Using the truth table, determine whether the following two propositions are logically equivalent: Question 2. Using the truth table, determine whether the following two propositions are logically equivalent: Question 3. Show that the following argument is invalid. Question 4: (a) Using the truth table, show that the argument is valid (Modus Ponens or the method of affirming) (b) Using the truth table, show that the argument is invalid Question 5: (a) Using the truth table, show that the argument is valid (Modus Tollens or the method of denial) (b) Using the truth table, show that the argument is invalid Question 6: (a) Using the truth table, show that the argument is valid (Hypothetical Syllogism) P+r Question 7: Example 4.8 Whai is the no of the rogonition Vc D,P) Question 8. Show that

Explanation / Answer

Question 1.

P v (q^r) and (p^q) v (p^r)

P

Q

R

P ^ Q

P ^ R

Q ^ R

P v (Q ^ R)

( P ^ Q) v ( P ^ R)

0

0

0

0

0

0

0

0

0

0

1

0

0

0

0

0

0

1

0

0

0

0

0

0

0

1

1

0

0

1

1

0

1

0

0

0

0

0

1

0

1

0

1

0

1

0

1

1

1

1

0

1

0

0

1

1

1

1

1

1

1

1

1

1

Since the values in last two columns is not same, the two propositions p v (q ^ r) and (p^q) v (p^r) are the logically equivalent.

Question 2.

P à (~Q ^ R) and ~P v ~ (R à Q)

P

Q

R

~P

~Q

~Q ^ R

R -> Q

~ (R -> Q)

P -> (~Q ^ R)

~P v ~ (R -> Q)

0

0

0

1

1

0

1

0

1

1

0

0

1

1

1

1

0

1

1

1

0

1

0

1

0

0

1

0

1

1

0

1

1

1

0

0

1

0

1

1

1

0

0

0

1

0

1

0

0

0

1

0

1

0

1

1

0

1

1

1

1

1

0

0

0

0

1

0

0

0

1

1

1

0

0

0

1

0

0

0

Since the values in the last two columns are same, the two propositions are logically equivalent.

P

Q

R

P ^ Q

P ^ R

Q ^ R

P v (Q ^ R)

( P ^ Q) v ( P ^ R)

0

0

0

0

0

0

0

0

0

0

1

0

0

0

0

0

0

1

0

0

0

0

0

0

0

1

1

0

0

1

1

0

1

0

0

0

0

0

1

0

1

0

1

0

1

0

1

1

1

1

0

1

0

0

1

1

1

1

1

1

1

1

1

1

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