TOMATO

Question

If A, B, C and D are statements such that if at least one of A and
B is true, then at least one of C and D must be true. Further, both A
and C are false. Then

(a) if D is false then B is false
(b) both B and D are false
(c) both B and D are true
(d) if D is true then B is true.

Comments

I think $option  \ a$ is correct

if $D$ is false, then $C$ and $D$ both are $false$

$A$ and $B$ are both $false$, $A$ is already $false$ then $B$ must be $false$ also

So, if $D$ is $false$, then $B$ will be $false$ also

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plz can u explain me why other options get discarded.as given in question when one of them is true i.e if B is true D can also be true.Rather we can also say that both can be true or false.

Plz kindly explain.

Answer 1

Option A is Correct.

Given Premises : $(A+B)\rightarrow (C+D)$ ; $\overline{A}; \overline{C}$

$A$ and $C$ are False, So, $B\rightarrow D$ and We know that Every implication sentence is Equivalent to its Contrapositive i.e. $\overline{D}\rightarrow \overline{B}$, Thus Option A is True.