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 thatExplanation / 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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