SOLUTION: Assume that the following 4 logical propositions are all true : 1. A → B 2. C → D 3. A ∨ C 4. ¬D What can you say about the truth value of propositions A, B,

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Question 1032455: Assume that the following 4 logical propositions are all true :
1. A → B
2. C → D
3. A ∨ C
4. ¬D
What can you say about the truth value of propositions A, B, C and D. You
can answer true, false, or uncertain. Justify your answers.
Truth value of proposition D :
Truth value of proposition C :
Truth value of proposition A :
Truth value of proposition B :
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
¬D is given to be true (premise 4). So the opposite of that, D, must be false.

Truth value of proposition D : false

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If D is false, then C -> D would be false if C were true. Since implications are false if the antecedent is true while the conclusion is false.

But we're given C -> D to be true. This forces C to be false

Truth value of proposition C : false
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In premise 3, A v C is assumed to be true. So either A is true or C is true.

Now that we know that C is false, we conclude that A must be true to make A v C true

Truth value of proposition A : true

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A -> B is true (assumption; premise 1)

A is true (see last section above)
To ensure that A -> B is true, we must force B to be true as well. If B were false, then A -> B would be false.


Truth value of proposition B : true


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Summary:

Truth value of proposition D : false
Truth value of proposition C : false
Truth value of proposition A : true
Truth value of proposition B : true
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