logically equivalent
1
When two statements are logically equivalent, the columns in the truth table under their main logical operators
Multiple Choice
• show neither statement is contingent.
• are exactly alike.
• are exactly opposite.
• show both statements are tautologies.
2
The “?” sign is used to symbolize
Multiple Choice
• “Either . . . or . . . but not both.”
• “If . . . then . . .”
• “Both . . . and . . .”
• “Either . . . or . . . or both.”
3
The truth table for a symbolized argument containing four statement letters will have
Multiple Choice
• 4 rows.
• 8 rows.
• 12 rows.
• 16 rows.
4
Which of the following is not a well-formed formula (WFF)?
Multiple Choice
• (~A ? B ? C)
• ~A ? (B ? C)
• ~(A ? B) ? C
• (~A ? B) ? C
5
Which of the following is not a condition for a symbolic expression to be a well-formedformula (WFF)?
Multiple Choice
• If p is a WFF, then so is ~(p).
• If p and q are WFFs, then so is (p • q).
• If p and q are WFFs, then so is (p ? q).
• If p and q are WFFs, then so is (p ? q).
6
In A ? B,
Multiple Choice
• A provides a necessary condition for B.
• B provides a sufficient condition for A.
• A provides a sufficient condition for B.
• A provides both a necessary and sufficient condition for B.
7
Where “F” stands for “Fred likes ice cream” and “L” stands for “Lou likes ice cream,” the statement “Neither Fred nor Lou likes ice cream” is best symbolized by
Multiple Choice
• ~F ? ~L.
• ~F • ~L.
• ~F ? ~L.
• ~(F • L).
8
Using a truth table, we can tell that an argument is valid if
Multiple Choice
• there is at least one row where the premises and conclusion are all true.
• there is no row where the premises are true and the conclusion is false.
• there is no row where the conclusion is false.
• there is at least one row where the premises are all true and the conclusion is false.
9
On which assignment of truth values does the sentence A ? ~B turn out to be false?
Multiple Choice
• A is true, and B is true.
• A is true, and B is false.
• A is false, and B is true.
• A is false, and B is false.
10
Under which assignment of truth values does the sentence A ? (B • ~C) turn out to betrue?
Multiple Choice
• A is true, B is false, and C is false.
• A is false, B is true, and C is false.
• A is false, B is false, and C is false.
• A is true, B is false, and C is true.
11
Under which assignment of truth values does the sentence (A ? ~B) • ~C turn out to betrue?
Multiple Choice
• A is true, B is false, and C is false.
• A is true, B is true, and C is false.
• A is false, B is false, and C is false.
• A is true, B is false, and C is true.
12
Where “F” stands for “Fred likes ice cream” and “L” stands for “Lou likes ice cream,” the statement “Fred doesn’t like ice cream only if Lou doesn’t like ice cream” is best symbolized by
rev: 09_02_2015_QC_CS-21722
Multiple Choice
• ~F ? ~L.
• ~F • ~L.
• ~F ? ~L.
• ~(F • L).
13
A compound statement is a contradiction if
Multiple Choice
• it is false regardless of the truth values assigned to the atomic sentences that compose it.
• its truth value is a function of the truth values of its component atomic sentences.
• it is true regardless of the truth values assigned to its component atomic sentences.
• its truth value is a function of the placement of its parentheses.
14
A compound statement is a tautology if
Multiple Choice
• it is false regardless of the truth values assigned to the atomic sentences that compose it.
• its truth value is a function of the truth values of its component atomic sentences.
• it is true regardless of the truth values assigned to its component atomic sentences.
• its truth value is a function of the placement of its parentheses.
15
Which of the following is an atomic statement?
Multiple Choice
• Sailing is an enjoyable sport.
• Sewing and cross-stitch require good eyesight.
• The Cincinnati Reds did not win their last game.
• Either Sue or Karen will get the high score.