Truth Values and Logical Implications

The video tutorial explains how to construct a truth table for the logical statement 'if not P then Q and R'. It begins by identifying the three variables involved and setting up the initial columns and rows. The tutorial then details how to fill in the columns for 'not P' and the conjunction 'Q and R'. Finally, it analyzes the implication 'if not P then Q and R', explaining when the implication is true or false based on the truth values of the components. The completed truth table is presented at the end.

What are the three variables used in the truth table for the statement 'if not p then q and r'?

• p, q, r

• x, y, z

• a, b, c

• m, n, o

How many rows are needed to list all possible permutations of truth values for three variables?

• 10

• 6

• 4

• 8

When is the column for 'not p' true?

• When p is true

• When p is false

• When q is true

• When r is false

What is the truth value of 'not p' when p is true?

• True

• False

• Cannot be determined

• Depends on q

Under what condition is the conjunction 'q and r' true?

• When both q and r are true

• When both q and r are false

• When q is false and r is true

• When q is true and r is false

In which rows is the conjunction 'q and r' true?

• Rows 7 and 8

• Rows 3 and 6

• Rows 2 and 4

• Rows 1 and 5

What is the truth value of 'q and r' in row 5?

• False

• True

• Cannot be determined

• Depends on p

When is the implication 'if not p then q and r' false?

• When not p is true and q and r is true

• When not p is false and q and r is false

• When not p is true and q and r is false

• When not p is false and q and r is true

In which rows is the implication 'if not p then q and r' false?

• Rows 2, 3, and 4

• Rows 6, 7, and 8

• Rows 4, 5, and 6

• Rows 1, 2, and 3

What is the truth value of the implication 'if not p then q and r' in row 1?

• True

• Cannot be determined

• Depends on other variables

• False