Discrete Math: Logic and Proofs

Negate the statement: "If q then not p"

Rewrite the English sentence "There is an adult in your neighborhood who knows kung-fu and karate" using predicates and quantifiers.

Rewrite the English sentence "There is an adult in your neighborhood who knows kung-fu but not karate" using predicates and quantifiers.

Rewrite the English sentence "Every adult in your neighborhood knows kung-fu or karate" using predicates and quantifiers.

Rewrite the English sentence "No adult in your neighborhood knows kung-fu or karate" using predicates and quantifiers.

Prove that no integer is both even and odd using proof by contradiction.

Prove that if $n^2$ is even, then $n$ is even using a proof by contrapositive.

Show that T is true from the following premises using rules of inference.

Prove $Q \land R$ given $P \implies Q \land R$ and $P$.

Prove $T$ is true given that $P \land Q$ is true, $P \lor S$ or $P \lor S \implies \lnot R$ is true, and $R \lor T$ is true.

Translate the following predicate logic statement to English: "$\forall x \forall y ( C(x, y) \land R(x, y) \Rightarrow L(x, y) )$".

Construct the truth table for the negation of a statement P.

Construct the truth table for the conjunction of two statements P and Q.

Construct the truth table for the disjunction (or) of two statements P and Q.