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Quiz about Conditional Statements AND Logical Connectives

Conditional Statements AND Logical Connectives Quiz

This quiz has questions relating to if-then statements, logical connectives (and, or, etc.), and a combination of both topics. These concepts are important not only in mathematics but also in fields such as philosophy and logic. Enjoy!

A multiple-choice quiz by EpicNight13. Estimated time: 5 mins.

Author
EpicNight13

Time
5 mins

Type
Multiple Choice

Quiz #
401,212

Updated
Dec 03 21

# Qns
10

Difficulty
Tough

Avg Score
5 / 10

Plays
227

Last 3 plays: Guest 198 (5/10), Guest 49 (4/10), Guest 143 (3/10).

One at a Time - Single Page

Question 1 of 10

1. Let P be the statement "If X, then Y." Which of the following statements describes the inverse of P? Hint

If Y, then X

If not X, then not Y

If not Y, then not X

If X, then not Y

NEXT>

Question 2 of 10

2. Suppose that the statement "If X, then Y" is true. Which of the following MUST also be true? Hint

If X, then not Y

If Y, then X

If not Y, then not X

If not X, then not Y

NEXT>

Question 3 of 10

3. Suppose that the converse of a conditional statement is false. Is the inverse of the conditional statement also NECESSARILY false?

Yes

NEXT>

Question 4 of 10

4. Let P be the statement "X or Y." Which of the following conditions makes P NECESSARILY false? Hint

Either X is false or Y is false, but not both

More information is needed

Both X and Y are true

Both X and Y are false

NEXT>

Question 5 of 10

5. Let P be the statement "X and Y." If X is false, is it NECESSARILY true that P is false?

Yes

NEXT>

Question 6 of 10

6. Let P be the statement "(X and Y) or Z." Suppose that P is true and Z is false. Which of the following MUST be correct? Hint

Either X is false or Y is false, but not both

More information is needed

Both X and Y are false

Both X and Y are true

NEXT>

Question 7 of 10

7. Let P be the statement "If X or Y, then Z." Which of the following is the inverse of P? Hint

If not Z, then not X and not Y

If X and Y, then not Z

If not X and not Y, then not Z

If not X or not Y, then not Z

NEXT>

Question 8 of 10

8. Let P be the statement "If not X and not Y, then not Z." Suppose that P is true. Which of the following MUST also be true? Hint

If X or Y, then Z

More information is needed

If not Z, then not X and not Y

If Z, then X or Y

NEXT>

Question 9 of 10

9. Let P be the statement "(X and Y) or (Y and Z)." Which of the following conditions makes the statement "not P" NECESSARILY true? Hint

X is false

Y is false

Z is true

Y is true

NEXT>

Question 10 of 10

10. Let P be the statement "If W, then X or (Y and Z)." Which of the following conditions, when true, would make P false? Hint

If W, then (not X and not Y) or (not X and not Z)

If W, then (not X or not Y) and (not X or not Z)

If W, then X and (not Y or not Z)

If W, then not X or (not Y and not Z)

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Dec 14 2024 : Guest 198: 5/10
Dec 13 2024 : Guest 49: 4/10
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Quiz Answer Key and Fun Facts

1. Let P be the statement "If X, then Y." Which of the following statements describes the inverse of P?

Answer: If not X, then not Y

"If Y, then X" is the converse of P.
"If not Y, then not X" is the contrapositive of P.

2. Suppose that the statement "If X, then Y" is true. Which of the following MUST also be true?

Answer: If not Y, then not X

"If not Y, then not X" is the contrapositive of the statement. The contrapositive of a conditional statement always has the same truth value as the original statement. Thus since the original statement is true, the contrapositive is also true.

3. Suppose that the converse of a conditional statement is false. Is the inverse of the conditional statement also NECESSARILY false?

Answer: Yes

Let P be the conditional statement "If X, then Y." The converse is "If Y, then X" and the inverse is "If not X, then not Y." Notice that the inverse is the contrapositive of the converse and so it shares the same truth value as the converse.

4. Let P be the statement "X or Y." Which of the following conditions makes P NECESSARILY false?

Answer: Both X and Y are false

In order for P to be false, both X and Y need to be false. If either X or Y is true, then P is true.

5. Let P be the statement "X and Y." If X is false, is it NECESSARILY true that P is false?

Answer: Yes

In order for P to be true, both X and Y must be true. If either is false, the entire statement is false.

6. Let P be the statement "(X and Y) or Z." Suppose that P is true and Z is false. Which of the following MUST be correct?

Answer: Both X and Y are true

Let Q be the statement "X and Y." Then P is "Q or Z." Since Z is false, the only way for P to be true is if Q is true; that is, "X and Y" is true. In order for "X and Y" to be true, both X and Y must be true.

7. Let P be the statement "If X or Y, then Z." Which of the following is the inverse of P?

Answer: If not X and not Y, then not Z

Let Q be the statement "X or Y." Then P is "If Q, then Z." The inverse of P is then "If not Q, then not Z," which is "If not (X or Y), then not Z. Since "not (X or Y)" is equivalent to "not X and not Y," the result follows.

8. Let P be the statement "If not X and not Y, then not Z." Suppose that P is true. Which of the following MUST also be true?

Answer: If Z, then X or Y

The contrapositive of P must also be true. Let Q be the statement "not X and not Y." Then the contrapositive of P is "If Z, then not Q." Since "not Q" is equivalent to "X or Y," the result follows.

9. Let P be the statement "(X and Y) or (Y and Z)." Which of the following conditions makes the statement "not P" NECESSARILY true?

Answer: Y is false

Notice that "not P" is the statement "(not X or not Y) and (not Y or not Z)." We then need "(not X or not Y)" and "(not Y or not Z)" to both be true. The result follows since "Not Y" being true (which means Y being false) guarantees that "not P" is true, while the others listed do not.

10. Let P be the statement "If W, then X or (Y and Z)." Which of the following conditions, when true, would make P false?

Answer: If W, then (not X and not Y) or (not X and not Z)

P will be false if "If W, then not (X or (Y and Z))" is true. Expanding "not (X or (Y and Z))" yields the result. The following are equivalent:
not (X or (Y and Z))
not X and (not (Y and Z))
not X and (not Y or not Z)
(not X and not Y) or (not X and not Z)

Source: Author EpicNight13

This quiz was reviewed by FunTrivia editor WesleyCrusher before going online.
Any errors found in FunTrivia content are routinely corrected through our feedback system.

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