# Tagged Questions

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### Negation of a proposition of the form “not(p) & q”

This is a homework question I'm working on. I think it's right but I'm just curious if I'm supposed to state the negation of "but it is always right" differently. Find the negation of the ...
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### Logical Notations for Mathematical Statements

I'm studying Discrete mathematics and I'm faced with a problem of converting a few descriptive mathematical statements into logical notation. Any help would be appreciated. Thank you. a). Any divisor ...
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### How can I use modus ponens or modus tollens to produce valid arguments? [closed]

I know this one is: $(1)$ If logic is easy, then I am a monkey’s uncle. I am not a monkey’s uncle. ∴ ? My answer: $\therefore$ Logic is not easy. (2) Can someone help me with this one? If ...
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### Write $p \rightarrow \lnot q$ in CNF form with only and ,or and brackets

Write $p \rightarrow \lnot q$ in CNF form with only and, or, and/or brackets How on earth would I even do this? Completely lost! Any help appreciated.
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### I have confusion while translating propostions to logical expressions

I have following propositions: p:Grizzly bears have been seen in the area. q:Hiking is safe on the trail. ...
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### tautologies and contradictions with $r$

I'm really struggling to understand tautologies and contradictions. I've been able to do $(p \rightarrow q) \leftrightarrow (\lnot q \rightarrow \lnot p)$ and I understand why it is a tautology, ...
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### I need to show the validity of the below arguments by using a truth table

I need to show the validity of $P \rightarrow Q$ $P \rightarrow R$ $\therefore P \rightarrow (R \wedge Q)$ Can i just show the truth table for $P \rightarrow Q$ and the truth table for ...
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### Discrete math proof issue

This is a question from my discrete math quiz. I was asked to prove there exists a Q(x). I used Disjunctive Syllogism to prove it. I was marked incorrectly because I used two different variables in ...
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### Proof methods Discrete Math

Claim: for any integers m and n, if $7m + 5n = 147,\,$ then $m$ is odd or $n$ is odd a) state the converse of the claim b) state the contrapositive of the claim. c) use proof by contrapositive to ...
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### Proving that $\{\to, \lnot\}$ is logically complete

Prove that $\{\to,\lnot\}$ is logically complete. It is known that $\{\land, \lor, \lnot\}$ is logically complete.
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### Rules of inference proofs

I have the following: Premise: {$p \lor q, q\rightarrow r,p \land s \rightarrow t, \lnot r, \lnot q \rightarrow u \land s$}, conclusion: $t$ I'm having a real hard understanding how to prove the ...