Statement I: Standard deviation of 9+ zD is Statement-Il: Statement- || Standard deviation a x coefficient of z|

Q: ~ (pV q) V (~ p ^ q) and ~p

A:

Q: Check this for validity using a partial truth table and explain why it is or isn't valid: (A v B),…

A: The logical connective "and" denoted by   p∧q is true only when both p and q are true. The logical…

Q: The replacement rule (a = -b): (a = b), though not part of Klenk's system, is a truth-preserving…

A: Given: a≡~b : : ~a≡b Here, a≡~b means a is agreed but not b. And ~a≡b means both a and b is not…

Q: Write the expression (P ^¬ Q) v (Q ^ P) as an implication or justify if it's not possible

A: The equivalent of implication is P→Q ⇔~P ∨ Q By DeMorgan's Law we have {\displaystyle \neg (P\lor…

Q: Explain what the truth value is of (a) ∃x(x+ x^4= −17) (b) ∀x(4x > x^4) with logic/reasons, whereas…

A: We will answer the second question as we don't answer multiple questions at a time and the first…

Q: Use a truth table to determine whether (p^ (qVr)) and ((p^q) V (p^r)) are logically equivalent.

A: We have to show that statements are logically equivalent.

Q: (e) There was a day last week when the temperature was at least forty degrees. (3) How do the final…

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Q: Does there exist false although its contrapositive Justify your answer. statement that is is true? a

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Q: Select the logical expression that is equivalent to:-3xv(A(x) B(x,y)) -(A(x) B(x,y))…

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Q: Select the proposition that is neither a ta b←(bvd) O b←(bnd) O Oq (pvq) b←(d-vd) O

A: Tautology and contradiction statement

Q: Consider the sentence P defined as follows: (‡n € Z+ : ) ((n 1)). (a) First, state the negation of…

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Q: how do i find p(AorB) when the question is P(A and B)= 0.4, P(A)=0.7, and P(B)=0.6 how do i find…

A: From the given information, P(A and B)=0.4, P(A)=0.7 and P(B)=0.6

Q: r be the statement Paris is the capital of France. p be the statement It is raining. Then using…

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Q: 3. Prove that (p A q) → ((¬p) → q) and (-p) V (¬q) are logically equivalent by using basic logical…

A: Given- (p∧q)→((¬p) ↔q)  and (¬p)∨(¬q) To prove- The above given prepositions are logically…

Q: If p represents "Unicorns once roamed the Ear and cheetahs are the fastest land animals."? Review…

A: p : Unicorns once roamed the earthq : cheetahs are the fastest land animals

Q: Consider statements p and q. p: Greg is singing. q: Salma is in art class. For parts (a) and (b),…

A: p: Greg is singing. q: Salma is in art class.

Q: Give the truth value of the sentence - (2 > 3) – (3 > 2) -- (3 > 2).

A: Let's find.

Q: (d) State whether or not P = Q, when P is the proposition (p → q) –→ (q ^ r) and Q is the…

A: Truth table: A truth table is a tabular representation of all the possible combinations of input…

Q: Using truth tables, determine if the following statements are tautologies or con- tradictions. (a)…

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Q: Consider statements p and q. p: Ahmad is studying. q: Maya is in math class. For parts (a) and (b),…

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Q: Use truth tables to show that the following statements are logically equivalent: (a) x^(y v z) =…

A: Using truth table to solve the subparts,

Q: Which is the contrapositive of A==> B? (a) B ==> A (b) -,B ==> A (c) -,B ==> -,A (d) -,A…

A: Which is the contrapositive of A==> B?

Q: Use a truth table to determine whether the statement below is a tautology, a self-contradiction, or…

A: We have, ~(~ q ^ p) <—> (q^~p)

Q: Suppose statements p and q are both false, and statements r and s have unknown truth values.…

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Q: why don't we use the existential instantiation(∃x) instead of the universal because it says "A car"…

A: A convertible car is anonymous, whose it is; which company; how many in the locality, city, country;…

Q: Select the law which shows that the two propositions are logically equivalent.…

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Q: This proposition is a tautology: [p^(p-q)]→q Show your proof using truth tables and by a series of…

A: To find- This proposition is a tautology: p ∧ p → q → q Show your proof using truth tables and by a…

Q: Attached

A: 18.  - represents Negation.-B represents the negation of B. So if B is false then -B is true/\…

Q: (b~vd) ^ (bvd~)

A: See next step for truth table

Q: Use De Morgan's laws to determine which one of the below expressions is equivalent to the following…

A: We have to find correct option by finding equivalent expression using given information. Concept…

Q: . Q1; Propositions and Connectives Determine whether the following propositional form is a…

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Q: What is the simplified logical expression of (p A q) → (p→q)? Answer:

A:

Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.