Problem 6. Let ? = {?, ?, ?, ?}. Define ? on ? as follows: ? = {(?, ?), (?, ?), (?, ?), (?, ?), (?, ?)} (a) Find the reflexive closure of R.

Q: B. Consider the following relation on {1, 2, 3, 4, 5} R1 = {(1,1), (1,2)(2,1)(2, 2), (3,4), (4,3),…

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Q: Given the following relation, { ( A, A ), ( A, B ), ( A, E ), ( B, B ), ( B, E ), ( C, A ), ( C, B…

A: Given the following relation, {(A, A), (A, B), (A, E), (B, B), (B, E), (C, A), (C, B), (C, C), (C,…

Q: If P(A)=p, P(A|B)=q, P(B|A)=r and A,B are mutually exclusive then what is the relation between p,q…

A: Let A and B be two events which are mutually exclusive. The probability that event B occurs provided…

Q: Show that if P(A|B)> P(A), then P(B| A) > P(B).

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Q: 2. Consider the following two relations on real numbers R₁ = {(a,b) = R² | a<b}, the lesser than…

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Q: 1. Let A = {blue, yellow, red}, B = of the relations below (a) determine if it is a function (b) if…

A: R1: D X B={(cat,blue),(cat,red)} So, {(cat,blue)} ⊂{(cat,blue),(cat,red)} Therefore R1 is a…

Q: 4. Let R be the relation {(1, 2), (1, 3), (2, 3), (2, 4), (3, 1)), and let S be the relation {(2,…

A: To find the composition of two relations R and S . the domain of S°R will be same as domain of R…

Q: Which of the following relations contain cach of the following pairs (1, 1), (1, 2), (3, 2), and…

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Q: The relation R₁ = {(a, b) = N²: alb} symmetric. O True False

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Q: 5. Let A = {a,b} and B = {1,2,3}. (a) Write out all functions f: A → B using two-line notation. How…

A: Note:-  As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: With domain of discourse as the real numbers, prove that the following statement is false: Væ3y(y? <…

A: the given statement states that for all real values of x there exist a real value y such that  y2…

Q: 4. R= {(x,y) x + y ≤ 8} reflexive irreflexive symmetric asymmetric anti- symmetric 1. 2. 3. 4. Which…

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Q: for the following relations on 2 the set A = {1, 2, 3}: R = {(1, 1), (1, 2), (1, 3), (3, 3)},…

A: A relation R is an equivalence relation if it is: i) Reflexive: if aRa for all a in A ii) Symmetric:…

Q: A = {5,6} B = {5, 7 ,8} S = {n | n >= 3 is an odd integer} A relation R from AxB to S is defined…

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Q: 11. Let A = {1,2,3,4} and B = {A, B, C, D, E}. Consider the following relations and state whether…

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Q: Given R, = {(1, 2), (2, 3), (3, 4)} R2 = {(1, 1), (1, 2).(2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3,…

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Q: Let F(x.y): "x is friend with y", N(x): "x is funny", W(x): "x is wise", R(x): "x is fair". The…

A: The symbolic is given as follows: ∃x∀y¬Nx∧Wx∧Ry→¬Fx,y We are given that: Fx,y: "x is friends with…

Q: Let the domain of x and y be all people. Let W(x): "x is a woman", M(y): "y is a man", and Lex.y):…

A: The objective is explain the meaning of the statement ∀x∀y Wx∧My→Lx,y

Q: Let P(x) be the propositional function “ x = x². Tell whether each p The domain of discourse is…

A: Introduction: A proposition is a collection of declarative statements with the truth value "true" or…

Q: 1. Let P (x) be the statement "x = x²." If the domain consists of the integers, give True/False…

A: We have given a statement ,  P(x) : x = x2 Here , domain consists of the integers , that is x ∈ ℤ.…

Q: Let A = (x = R: 7 ≤x < 20} and B = {7, 18, 19, 20, 21). What is A - B? A. {x ER: (7<x< 18) (18 < x…

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Q: Define a relation R on Z as follows: For all integers m and n, 51(m² - n²). mRn (a) Is 1 R (-4)? Yes…

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Q: How many relations are the

A: Given : The set is { 1, 2} .

Q: 2. Definition. Let r be a non-negative positive real numbel A square root of r is the Iinique…

A: Note: Square of any real number must be non-negative and addition or subtraction of any two real…

Q: How many symmetric relations on the set A = {1,2, 3, 4, 5, 6, 7, 8} contain the ordered pairs (2,…

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Q: . Given the relation R1 from X = {1,2,3,4} to Y = {a,b,c} and R2 from Y = {a,b,c} and Z = {6,7,8}…

A: Here given  Relation R1 from X=1, 2, 3, 4 to Y=a, b, c is defined as R1=1, a, 2, a, 2, b, 3, c, 4,…

Q: Write the mathematical formulas corresponding to the following statement with the help of the…

A: Given statement : Every function with positive and negative values has a root.

Q: Let the domain be the set of all integers. Is the following predicate statement true or false? ∀x∃y…

A: Given that the domain be the set of all integers. And we have to verify that the given statement is…

Q: Let F(x.y): "x is friend with y", N(x): "x is funny", W(x): "x is wise", R(x): "x is fair". The…

A: Given: The functions Fx,y: "x is friend with y". Nx: "x is funny". Wx: "x is wise". Rx: "x is…

Q: a. Construct an interpretation (i.e., give the domain and the meaning of P(x)) in which (∀x)P(x) has…

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Q: let a and m be the integers with gcd(a,m)=1, what is the relation between ord m (a) and ord m (-a)

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Q: 3. Let R1 = {(1, 2), (2, 3), (3, 4)} and R2 = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3,…

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Q: QUESTION 1 Let F(x.y): x is friend with y". N(x): "x is funny", W(x): "x is wise". R(x): x is fair".…

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Q: 6. Based on what you know about the multiplicative principle, how many functions f:A- Bare there if…

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Q: Let F(x,y): "x is friend with y", N(x): "x is funny", W(x): "x is wise", R(x): "x is fair". The…

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