Contrapositive Study guides, Class notes & Summaries

What is the notation for subset? ⊆ A collection of objects is known as a set What is the notation for integers? ℤ What is the notation for element? ∈ What is the notation for set-roster? { } Write the set-builder notation for, "Numbers whose square roots are an integer" { x | √x ∈ ℤ} Write the set-builder notation for "the set of all x's, such that x is greater than 0" { x | x > 0} T/F: Order matters in ordered pairs? T...

WGU C959 - Discrete Math Questions and Answers Rated A+ What is the notation for subset? ⊆ A collection of objects is known as a set What is the notation for integers? ℤ What is the notation for element? ∈ What is the notation for set-roster? { } Write the set-builder notation for, "Numbers whose square roots are an integer" { x | √x ∈ ℤ} Write the set-builder notation for "the set of all x's, such that x is greater than 0" { x | x > 0} T/F: Order matters in ordered pairs?...

LSAT Prep Question with complete solution 2024Lesson 1 - correct answer ... Argument - correct answer Consists of a conclusion and a set of premises given in support of that conclusion Set of Facts - correct answer A group of statements from which no conclusion is drawn. Valid Conclusion - correct answer A statement that must be true according to the premises Invalid Conclusion - correct answer A statement that is not necessarily true according to the premises Assum...

WGU C959 unit 1 latest 2023 already passed p∧q conjunction "and" T/T=T T/F=F F/T=F F/F=F p∨q disjunction/inclusive or "or" T/T=T T/F=T F/T=T F/F=F p⊕q exclusive or "or" T/T=F T/F=T F/T=T F/F=F ¬p negation "not" ¬T = F ¬F = T p→q conditional operation "if p then q" T/T=T T/F=F F/T=T (p=F, q=T regardless of truth value) F/F=T converse of p→q q→p contrapositive of p→q ¬q→¬p inverse of p→q ¬p→¬q p↔q biconditional operation "if and only if" T/T=...

Proof by Exhaustion Prove the statement by checking each element individually. Unlike proof by cases, exhaustive proof looks at every case in a way that is not general. Proof by Counterexample Used to disprove a universal statement. For example, to disprove the statement, "All prime numbers are odd" find one example where this statement is false—the number 2—which is both even and prime. Direct Proof In the direct proof, we assume the hypothesis p is true and we try to pro...

Exclusive or. ⊕ One or the other, but not both. We can go to the park or the movies. inclusive or is a: disjunction Order of operations in absence of parentheses. 1. ¬ (not) 2. ∧ (and) 3. ∨ (or) the rule is that negation is applied first, then conjunction, then disjunction: truth table with three variables see pic 2^3 rows proposition p → q Ex: If it is raining today, the game will be cancelled. Converse: q → p If the game is cancelled...

p∧q conjunction "and" T/T=T T/F=F F/T=F F/F=F p∨q disjunction/inclusive or "or" T/T=T T/F=T F/T=T F/F=F p⊕q exclusive or "or" T/T=F T/F=T F/T=T F/F=F ¬p negation "not" ¬T = F ¬F = T p→q conditional operation "if p then q" T/T=T T/F=F F/T=T (p=F, q=T regardless of truth value) F/F=T converse of p→q q→p contrapositive of p→q ¬q→¬p inverse of p→q ¬p→¬q p↔q bicondi...

implication order correct answers ~, ^, v, -> <-> exclusive or correct answers (p ^ ~q) v (~p ^ q) p-> q converse, inverse, and contrapositive correct answers q->p, ~p->~q, ~q->~p what is value of p->q if p = 0` correct answers true definition of implication correct answers p → q ≡ ¬p ∨ q negation of p->q correct answers p ^ ~q P⟺q is the same as correct answers p → q ^ q → p r is a sufficient condition for s correct answers if r then ...

PropositionA declarative sentence that is either true or false. ConjunctionAnd, ∧ DisjunctionOr, ∨ Implication Converse p->qFlip q->p Contrapositive p->qFlip and negate ¬q -> ¬p Inverse p->qNegate

Definition: Premise - ANSWER-a supporting statement Definition: Conclusion - ANSWER-a supported statement Definition: Argument - ANSWER-two or more statements where on statement is supported by the other(s) Definition: Assumption - ANSWER-a premise left out of the argument Definition: Context - ANSWER-background information which is not used in the argument except as a referent Definition: Contrapositive - ANSWER-a logically equivalent statement derived from negating the necessary...