Prove R is irreflexive iff R ∩ idA = ∅. If idA={ ∈ A x A |a=b}

Q: Suppose R and S are relations from A to B. Must the following statements be true? Justify your…

A: Here I used counter example to show that the statement one is false and give the proof for statement…

Q: Given that S = {x|x €NAr < 20} and A, B, C C S with {r |3|r} {r|x | 560} {x|gcd(r, 110) = 1} A where…

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Q: Prove that ∀y ∈ Σ*, P(y) is true, where P(y) is the statement "∀y ∈ Σ*, r(xy) = r(y)r(x)".

A: Given : P(y) is the statement "∀y∈∑*, rxy=ry rx" To prove : ∀y∈∑* , P(y) is true Pre-requisite : The…

Q: Let AB = AC. Prove that if det(A) = 0, then B = C.

A: The given question Let AB = AC. Prove that if det(A) = 0, then B = C. this question is not correct…

Q: Give a natural deduction proof of 3 x A(x) V 3x B(x) →3x (A(x) V B(x)).

A: To prove: ∃xAx∨∃xBx→∃xAx∨Bx

Q: (c) Prove that r| +11 36 T-1 2 +36 for all real I.

A: We have to prove that the following inequality holds: x-11x2+36≤x+1136 for all real x. We will use…

Q: Premises: p → (q ^r), s → r, r → p. Prove: s→ q.

A: Since you have posted multiple questions and we can answer one question. So answer provided for…

Q: Prove that each argumentation below is valid using Natural Deduction: 1. Vx. (T(x) V S(x)) T(a) :.…

A: Disclaimer: Since you have asked multiple question, we will solve the first question for you. If you…

Q: Z Let AABC and ADEF have corresponding pairs of sides which are parallel. Say, AB || DE,BC || EF, AC…

A: given triangles are    △ABC  and   △DEF Also,       AB||DE,   BC||EF,   AC||DF yes it follows that…

Q: 6. Let A = {x EZ|x= 5a+2 for some integer a}, B = {y €Z|y= 10b – 3 for some integer b}, and C = {z…

A: Here  A =x∈Z| x=5a+2 for some integer a ,B=y∈z|y=10b-3 for some integer b    C=z∈Z | z=10c+7 for…

Q: Let f: [a,b]-R be afunction and let c<0, then for any Ac[a,b] sup cf=c inf f

A: We will prove it

Q: Show each of the following is valid using Rules of Inference and Laws of Equivalence: r v ~p -p = s

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Q: Let A = {x € R : x < a} and B={x €R: x < b}, where a and b are real numbers. Show that sup(A+ B) =…

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Q: The transitive property of equality states that if AB = BA, then BA = AB. %3D %3D O True O False

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Q: Need a formal proof: Show: Let x,y ∈ R. Then | |y| - |x| | ≤ |y-x|. Hint:a = |x|, b=|y| and ε =…

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Q: Q 2. Which set of information could not be used to prove AABC = ARST? B A R AB = RS, AC = RT, and ZC…

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Q: Let AB = AC. Prove that if det(A) + 0, then B = C.

A: Given: Let AB=AC. To Prove: If detA≠0, then B=C

Q: Suppose that the manufacturer of a gas clothes dryer has found that when the unit price is p…

A: topic - functions

Q: Let f:[a,b]-R be afunction and let c<0, then for any A C [a,b] sup cf =c sup f ulgn O ihi O

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Q: Let A ∈ (R) be given If A is nonsingular, prove that adj(A) is nonsingular and adj(A)^-1 = (A^-1)

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Q: prove the following : a) a0=0 b) (-a)v=a(-v)=-av c) av=0 implies either a=0 or v=0

A: What is Identity and Inverse Element: Identity element is that element which on performing binary…

Q: Let​ R(x), C(x), and​ P(x) be,​ respectively, the​ revenue, cost, and​ profit, in​ dollars, from the…

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Q: Let jEZ (a) Prove directly the statement : If 3j, then 3j²

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: Prove A X (BUC) - (Ax B) U (A x C)

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Q: 3. Show by an example that the following statements are false. i. a - (b c) = (a - b) (a - c) for…

A: ( i )  a - (b • c) = ( a - b ) • (a - c )  fo all a , b , c belongs to real number R   We show that…

Q: o P(A) < P(B), if A is in B. 0 P(A) = P(B), if A = B (i.e. A is in B and B is in A) Please discuss…

A: given that if A is in B then    P(A)≤P(B) now,…

Q: Let the universe of discourse be R. Prove that ∀x∀y [(x < y) → ∃z(x < z < y ∧ z ∈ Q)

A: Let the universe of discourse be R. Prove that ∀x∀y [(x &lt; y) → ∃z(x &lt; z &lt; y ∧ z ∈ Q)

Q: Prove that each argumentation below is valid using Natural Deduction: 1. Vx. (T(x) v S(x)) -T (a) :.…

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

Q: Let f:[a,b]→R be afunction and let c<0, then for any A C[a,b] sup cf =c sup f ylgn

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Q: Prove by resolution that "John likes peanuts" if you have these sentences in the knowledge base: -…

A: Answer is mentioned below

Q: p) Prove that if ac | bc and c +0 then a | b.

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Q: Translate these statements into English, where R(x) is "x is a rabbit" and H(x) is "x hops" and the…

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Q: Prove the following statements: i. {x €R : |x – 4| = 2|x| – 2} ={-6,2}

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Q: (b) If r23= 1, prove that R² (23) = 112=113 and 01.23 = 01 (1-12).

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Q: Identify the axiom or postulate that applies to the following statement.     If  x = AB + CD + EF +…

A: We have used the axioms here......

Q: Prove that for any positive numbers a and b the inequality ab+ba≥2 is valid.

A: It is required to prove for any positive numbers a and b.

Q: Prove that if A={- :n EN, then A' ={0}. Hint: (a) if x1, then . (d) if x=0, then x EN.

A: A set A=1n:n∈N then A'=0. i.e. the set of limit point contains only 0 element.

Q: Let x e R. Use the method of proof by contraposition to prove hat if x² – 6x + 8 > 0, then x > 4 or…

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Q: If A is 3 x 3 and det (A) = 0, then select all of the following statements which are true:

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Q: Define sets A and B of integers as follows: A= {neZ\n=5r for some integer r} B= {me Z|m=3s for some…

A: Set theory is a special branch of mathematics. A set is a well defined collection of objects. A set…

Q: Find B and A such that o(x) is continous: o(x)= {13-Bx.     x<-5}           {3x^2 -1.   -5 less…

A: The given piecewise function is: ox=13-Bx      for  x&lt;-53x2-1        for   -5≤x&lt;42x+A…

Q: Prove. 'if 0 < a ≤ b, then a2 ≤ b2 and √a ≤ √b.'

A: According to question,Given condition,0&lt;a≤b

Q: Prove that if A,B ∈Mn×n(F) are similar, then det(A) = det(B).

A: If the matrices A and B are similar then there exists a non singular matrix S,

Q: Prove that if a is odd and b is odd, then (a + 1) b is even

A: Number system.. properties

Q: Translate these statements into English, where R(x) is "x is a rabbit" and H(x) is "x hops" and the…

A:

Q: For all sets X, Y and Z use the element argument method to prove (X – Y) n (Y – Z) n (Z – X) = 4.

A: let X,Y,Z be any sets  claim- by using element argument method prove that X-Y∩Y-Z∩Z-X=∅