Idempotent law - Study guides, Class notes & Summaries

p v q This is a disjunction: p or q, or p and q. This is an inclusive or. p ^ q This is a conjunction: p and q p ⊕ q This is an exclusive or: either p or q p → q This is an implication. If p, then q Converse conditional statements q → p Contrapositive conditional statements ¬q → ¬p (has the same truth values as p → q) Inverse conditional statement ¬p → ¬q p ↔ q This is a biconditional statement, also known as bi-implicati...

Conjunction The conjunction "p and q" is denoted by p∧q. The conjunction p∧q is true when both p and q are true and is false otherwise. Disjunction The disjunction "p or q" is denoted by p∨q. The disjunction p∨q is false when both p and q are false and is true otherwise. Exclusive Or (XOR) The exclusive or "p xor q" is denoted by p⊕q. The exclusive or p⊕q is true when exactly one of p or q is true and is false otherwise. Conditional Statement (Implica...

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=...

WGU C959 (2023/2024) – Complete and Accurate Proposition T/F statement exclusive or AꚚB inclusive or/disjunction AꓦB conjunction AꓥB What is the precedence for compound propositions? quantifier > not > and > or > conditional/bi-conditional Rows in truth table with N variables? 2^N When are conditionals true/false? If p(T) then q(T) = T If p(T) then q(F) = F If p(F) then q(T) = T If p(F) then q(F) = T Biconditional iff, ↔ tautology compound proposition that is alway...

Tautology Compound proposition that is always true regardless of the truth value of individual propositions (Always ends up true) Contradiction Compound proposition that is always false regardless of the truth value of individual propositions (Always ends up false) Logical Equivalence When two different compound propositions have the same results for inputs Idempotent Propositional Law: PvP = P, P^P = P ('^' represents And) Associative Propositional Law: (PvQ)v...

Tautology Compound proposition that is always true regardless of the truth value of individual propositions (Always ends up true) Contradiction Compound proposition that is always false regardless of the truth value of individual propositions (Always ends up false) Logical Equivalence When two different compound propositions have the same results for inputs Idempotent Propositional Law: PvP = P, P^P = P ('^' represents And) Associative Propositional Law: (PvQ)v...

COSC 2425 Final Exam 67 (base 10)= __________________(base 3) - Answer- 2111 728 (base 9)= __________________(base 10) - Answer- 593 1101101 (base 2) = ____________ (base 10) - Answer- 109 01AF (base 16) = ____________ (base 10) - Answer- 431 Convert 0.2578125 to binary with 8 bits to the right of the binary point. - Answer- 0. Convert 0B2C (base 16) to binary. - Answer- Convert -47 (base 10) to binary 8-bit signed-magnitude. - Answer- Assuming we are using the Hamming ...

Introduction to Discrete Structures Final Exam Study Guide Solutions Logical Equivalence: Commutative Laws - ANSWER-p∧q ≡ q∧p p∨q ≡ q∨p Logical Equivalence: Associative Laws - ANSWER-(p∧q) ∧ r ≡ p ∧ (q∧r) (p∨q) ∨ r ≡ p ∨ (q∨r) Logical Equivalence: Distributive Laws - ANSWER-p ∧ (q∨r) ≡ (p∧q) ∨ (p∧r) p ∨ (q∧r) ≡ (p∨q) ∧ (p∨r) Logical Equivalence: Identity Laws - ANSWER-p∧t ≡ p p∨c ≡ p Logical Equivalence: Negation Laws...