Question 1032455
<font color=blue>ŹD</font> is given to be true (premise 4). So the opposite of that, D, must be false.


Truth value of proposition D : <font color = red>false</font>


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If D is false, then <font color=blue>C -> D</font> 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 <font color=blue>C -> D</font> to be true. This forces C to be false


Truth value of proposition C : <font color = red>false</font>

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In premise 3, <font color=blue>A v C</font> 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 <font color=blue>A v C</font> true


Truth value of proposition A : <font color = red>true</font>


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<font color=blue>A -> B</font> is true (assumption; premise 1)


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



Truth value of proposition B : <font color = red>true</font>



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Summary:


Truth value of proposition D : <font color = red>false</font>
Truth value of proposition C : <font color = red>false</font>
Truth value of proposition A : <font color = red>true</font>
Truth value of proposition B : <font color = red>true</font>