(2) -R 1) K = R 2) KƆ (RƆ P) 3) ~P P

Q: give the negation and contrapositve  of   'Everthing that is discrete is mathematics'.

A:

Q: Create a truth table for the expression (make sure you focus on the order of operations) and…

A: Given, The expression ~(~p → q) ⟷ p ∧ q ⋁ ~p

Q: What equivalence/law was applied? [(p → q) ^ (q → r)] → (p → r) = -[(p → q) ^ (q → r)] v (p → r) O…

A: Please check step 2 for the solution.!

Q: Simplify p A~(p ^~q).

A: Truth table :  It shows how the truth or falsity of a compound statement depends on the truth or…

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A: (a) Every student has a friend who is in the soccer team.  (b) all students in the tennis team has a…

Q: Verify the equivalences using truth tables. (p∨q)∧(¬p∨r)→ (q ∨r)is a tautology

A: Solution:

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A:

Q: Choose the proper symbol to make the sentence true -(-2)|-4| ___ -4|-2|. Single choice. > < =

A: Given,     -(-2)|-4| ___ -4|-2|   We need to put sign in the blank.

Q: II. Write as an English sentence and determine if it is true or false. 8. VXER, 3YER. x+y=10 9.…

A: 8)  Given, ∀ x ∈ℝ, ∃ y∈ℝ, x+y=10 Solution: For every x in ℝ(Real Numbers) there exist y in ℝ such…

Q: 3. We want to find S so ((A = B) A B) = S is a tautology. A B (A=B) A B TT ((A = B) ^ B) = S S TF FT…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: Use the rules of implication and rules of replacement to derive the conclusion given. Be sure to…

A:

Q: Using semantic tableaux, find whether the following formula is a tautology:…

A: To prove that a formula is tautology, we begin with the node as false.   The rules for conditional…

Q: What equivalence/law was applied? [-p v (p A ¬q)] v [r v (q ^ ¬r)] = [(¬p v p) ^ (-p v ¬q)] v [(r v…

A:

Q: Determine which pairs of actions are commutative.  “taking a test” and “studying for the test”

A: To determine Which pairs of actions are commutative.   “taking a test” and “studying for the test”

Q: Determine whether the statement forms are logically equivalent. In each case, construct a truth…

A: Given statement is,

Q: Verify the logical equivalence using laws of logics. Supply a reason for each step. ~((~p Λ q)ν (~p…

A:

Q: The statement: VyJx. P(x, y) =→ JæVy. P(x, y) is not valid. Choose the most reasonable method for…

A:

Q: Determine whether the statement forms are logically equivalent. In each case, construct a truth…

A: Given statement is,

Q: Prove validity: W → Z -Z

A:

Q: ing Equivalence Laws, show that - a) ¬(¬p ∧ q) ∧ (p ∨ q) is logically equivalent to p. b) ¬(p ∨ ¬( p…

A: Given, a ¬¬p∧q∧p∨q is to be shown logically equivalent to p.b¬p∨¬p∧q is to be shown logically…

Q: State whether the following set of statements is consistent or inconsistent. Explain your answer by…

A: Inconsistency: A set of statements is inconsistent if they are not all be true. If I says, "everyone…

Q: actor the folOwing expresSsion completely: expression comple w² – 20w 24 = - -

A:

Q: Insert either ⊆ or c/ in the blank space between the sets to make a true statement. {6, 8, 10, . .…

A: We can answer the question in the below steps.

Q: be filooing (P→9)+- P)

A: In the given question we have to simplify the following1.(p→q)↔(~q→~p)2.(p∧p)∨(q∧q)3.[~p∨(~q∧r)] i…

Q: (png)→p=T b. -p→F = p а.

A:

Q: Determine whether the statement forms are logically equivalent. In each case, construct a truth…

A: We need to determine whether the given statement forms are logically equivalent or not.So, the truth…

Q: Using appropriate laws of equivalence, demonstrate that (p→r)∨(q→r)≡(p∧q)→r Prove your answer…

A:

Q: A) Which property/properties of the equivalence relation R is used to prove the left-to-right…

A: If you observe carefully, you will see that they have used symmetric and transitive properties of…

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

A: The objective is to prove that the replacement rule  a≡~b : : ~a≡b is a truth preserving rule.

Q: (a) Use one of DeMorgan's Laws to choose a statement equivalent to the following. It is not the case…

A: Solution: The objective is to write the equivalent and negation statements

Q: Determine whether these statement forms are logically equivalent. In each case, construct a truth…

A: Boolean algebra is a branch of mathematics that is concerned with binary variables and operations on…

Q: • The domain for variables a and y is the set of students in a class. • The predicate R(x, y) means…

A:

Q: Write down the difference between contradiction and contigency with example.

A:

Q: Choose the correct answer: 2- The sense relation between skirt and trousers is: a. binary antonymy…

A: The sense relation between skirt and trousers is converseness.

Q: 25. Using appropriate laws of equivalence, demonstrate that -s-(-p V (-s→¬q)) = s V -p V Prove your…

A:

Q: Verify the equivalences using logical equivalence Show that ( ~q ^ (p  →  q))  →  ~p is a…

A:

Q: Translate the following argument into a first-order language: Every instance of knowledge is an…

A: To translate the given arguments into first-order language.

Q: Let x and y be bits. We want to find expression following truth-table.

A: Introduction:

Q: F ((p -> q) v (q -> r) -> (p -> r)) Say if it is tautology, contradiction or contingency

A:

Q: Determine whether the statement forms are logically equivalent. In each case, construct a truth…

A: Given statement is,

Q: Determine whether the statement forms are logically equivalent. In each case, construct a truth…

A: Recall the following fact.

Q: Use a truth table to determine whether the two statements are equivalent. -p--q, q-p Construct a…

A: The proposition ~p → ~q is called the inverse of p → q .

Q: Supply a reason for each step to show that the statement p→(q∨p) is a tautology. (Negation,…

A: We will find out the required solution.

Q: 2. Consider the statement. VrVyz(xyz). (a) (3 points) Rewrite this statement as a sentence Summer…

A: Please see the attachment

Q: Show that (p->q) ^ (p->r) is a contingency

A: Solution: The definition of Contingency - A Contingency is a proposition that is neither a tautology…

Q: Let P(a, b) and Q(a, b) be the open sentences defined by P(a, b) : a = b and Q(a, b) : a^2 − b^2 =…

A:

Q: Determine whether the statement forms are logically equivalent. In each case, construct a truth…

A:

Q: The diagram shows the relationship between two sets. Tulips aUse the diagram to write a statement…

A: We have to choose the correct statement.

Q: c) Show that (p ∨ q) ∧ (r ∨ ¬ q) → (p ∨ r) is a tautology. Ensure that you explain the steps taken…

A:

Q: c) Show that (p V q) ^ (r V ¬ q) → (p V r) is a tautology. Ensure that you explain the steps taken…

A: To show that p∨q∧r∨¬q→p∨r is a tautology. To prove this, it is necessary to prove all values are…