Contrapositive Corner

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Logic proof by contrapositive

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Raelii

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Froggy Jumps Contrapositive CornerVersión en línea Logic proof by contrapositive por Raelii 1 What is the contrapositive of a statement P → Q? a If P, then Q b If not Q, then not P c If Q, then P 2 If a false premise leads to a conclusion, what does contrapositive help us show? a Contradiction invalidates the proof b The contrapositive may be true even if the original seems false c The original is always true 3 Which is equivalent to P → Q? a P ∧ Q b ¬Q → ¬P c P ∨ Q 4 To prove P → Q using contrapositive, you prove: a ¬Q → ¬P b P → ¬Q c P ∧ Q 5 If it is not true that Q, what can we conclude about P in the contrapositive? a Q must be true b P is not necessarily true; we conclude ¬P c P must be true 6 Which of these is a valid contrapositive step? a Assume ¬P and derive Q b Assume P and derive Q c Assume ¬Q and derive ¬P 7 Contrapositive is a logical equivalence because: a P → Q is always true b P → Q is true iff ¬Q → ¬P is true c ¬P → ¬Q is equivalent 8 In a proof, can contrapositive be used when P → Q is not easily shown directly? a Yes, often easier to prove ¬Q → ¬P b No, never c Only with direct proof 9 Which statement is the contrapositive of 'If it rains, the street is wet'? a If the street is not wet, it did not rain b If the street is wet, it did not rain c If it rains, the street is dry 10 Which best describes contrapositive proof? a Prove ¬Q → ¬P to conclude P → Q b Prove P ∧ Q c Prove P → ¬Q

Froggy Jumps

Contrapositive CornerVersión en línea

Logic proof by contrapositive

por Raelii

What is the contrapositive of a statement P → Q?

If P, then Q

If not Q, then not P

If Q, then P

If a false premise leads to a conclusion, what does contrapositive help us show?

Contradiction invalidates the proof

The contrapositive may be true even if the original seems false

The original is always true

Which is equivalent to P → Q?

P ∧ Q

¬Q → ¬P

P ∨ Q

To prove P → Q using contrapositive, you prove:

¬Q → ¬P

P → ¬Q

P ∧ Q

If it is not true that Q, what can we conclude about P in the contrapositive?

Q must be true

P is not necessarily true; we conclude ¬P

P must be true

Which of these is a valid contrapositive step?

Assume ¬P and derive Q

Assume P and derive Q

Assume ¬Q and derive ¬P

Contrapositive is a logical equivalence because:

P → Q is always true

P → Q is true iff ¬Q → ¬P is true

¬P → ¬Q is equivalent

In a proof, can contrapositive be used when P → Q is not easily shown directly?

Yes, often easier to prove ¬Q → ¬P

No, never

Only with direct proof

Which statement is the contrapositive of 'If it rains, the street is wet'?

If the street is not wet, it did not rain

If the street is wet, it did not rain

If it rains, the street is dry

Which best describes contrapositive proof?

Prove ¬Q → ¬P to conclude P → Q

Prove P ∧ Q

Prove P → ¬Q

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Contrapositive Corner

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Contrapositive CornerVersión en línea

por Raelii

What is the contrapositive of a statement P → Q?

If a false premise leads to a conclusion, what does contrapositive help us show?

Which is equivalent to P → Q?

To prove P → Q using contrapositive, you prove:

If it is not true that Q, what can we conclude about P in the contrapositive?

Which of these is a valid contrapositive step?

Contrapositive is a logical equivalence because:

In a proof, can contrapositive be used when P → Q is not easily shown directly?

Which statement is the contrapositive of 'If it rains, the street is wet'?

Which best describes contrapositive proof?

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