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I am looking for some to explain what does this question want from me to do?

Determine all true value assignments, if any, for primitive statements $p, q, r, s, t$ that make each of the following compound statements false. Note: Do not answer this question by drawing truth tables. Study the compound statements and THINK about the truth values of the primitive statements. Your answers should be in English sentences.

a. $(p \land q) \land r \implies s \lor t$

b. $p \land (q \land r) \implies s \oplus t$ (where $\oplus$ means exclusive or)

Please note that I do not want the answer I want some one explains for me what does this question mean and what does it want from me?

This is my first math course. So consider that in mind!

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    We could cheat and compute the truth table, but that would be lengthy. Part of the point is that for some sentences, you can, by *thinking*, determine quickly the limited set of circumstances under which the sentence is false.2012-01-29

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Let me illustrate what’s wanted by working a similar problem. Suppose that the same question were asked about the compound statement $(p\land q)\to (s\lor t)$. An implication $A\to B$ is false if and only if $A$ is true and $B$ is false, so you want to ask yourself under what conditions on $p,q,s$, and $t$ will $p\land q$ be true and $s\lor t$ false. In words, $p\land q$ is true precisely when $p$ and $q$ are both true, and $s\lor t$ is false precisely when $s$ and $t$ are both false. We conclude, therefore, that

$(p\land q)\to (s\lor t)$ is false precisely when $p$ and $q$ are both true and $s$ and $t$ are both false.

As I read the question, this is the kind of answer that is wanted. Does that help?

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    @MIH1406: Yes. Under what circumstances to those implications become false. And your answer should be an English sentence that describes the truth values of $p,q,r,s$, and $t$ that make them false.2012-01-29
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Let's understand this with an example:

If $p,q,r,s,t$ are True then (a) is

(True and True and True)$\to$ (True or True)

which simplifies to

True $\to$ True

which is a true statement. (b), on the other hand evaluates to

(True and True and True)$\to$ (True xor True)

which simplifies to

True $\to$ False

which is a false statement (rememeber the truth table of $\to$).

You are asked to find all the values of $p,q,r,s,t$ such that (a) evaluates to True.