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reduction example

Explore the conditions under which a logical conclusion is false and learn to identify invalid arguments. Understand the truth table and premise combinations necessary for a valid conclusion.

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reduction example

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  1. reduction example

  2. r q s < < p r ~ ( m p ) ∴ q

  3. F r q s < < p r ~ ( m p ) F ∴ q the only conditions under which the conclusion is false

  4. there is more than one way to make this true. Do NOT start here. there is more than one way to make this true. Do NOT start here. F r q s < < p r ~ ( m p ) F ∴ q the only conditions under which the conclusion is false

  5. The only way to make this true F r q s < < p r ~ ( m p ) F ∴ q the only conditions under which the conclusion is false

  6. The only way to make this true is to make this false F r q s < F < p r T F ~ (m p) F ∴ q the only conditions under which the conclusion is false

  7. T F r q s < F T < p r the only condition under which this premise is true T F ~ ( m p ) F ∴ q the only conditions under which the conclusion is false

  8. T F r q s < Be careful, there are two possibilities: s might be false or s might be true F T < p r T F ~ ( m p ) F ∴ q the only conditions under which the conclusion is false

  9. T F r q s < Be careful, there are two possibilities: s might be false or s might be true There are two rows of the truth table on which the conclusion is false and premises 2 and 3 are true F T < p r true T F ~ ( m p ) true F ∴ q false

  10. T F T true r q s < Be careful, there are two possibilities: s might be false or s might be true There are two rows of the truth table on which the conclusion is false and premises 2 and 3 are true We are interested only in the possibility that all premises are true when the conclusion is false. F T < p r true T F ~ ( m p ) true F ∴ q false

  11. T F T true r q s < Be careful, there are two possibilities: s might be false or s might be true There are two rows of the truth table on which the conclusion is false and premises 2 and 3 are true We are interested only in the possibility that all premises are true when the conclusion is false. F T < p r true T F ~ ( m p ) true F ∴ q false This argument is INVALID WHEN IT IS POSSIBLE TO MAKE A PREMISE false OR true , YOU MUST MAKE IT TRUE .

  12. ∴ ∴ < < < <

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