Let P(x; y) : x plays in y A(x) : x is athletic. S(x) : x is smart.  E(y) : y is in English league.  F(y) : y is famous.  Assume the domain of x is all players and the domain of y is all football teams. The symbolic of the following statement "Some smart players play in all famous teams " is :      1.     for all x there exists y space S left parenthesis x right parenthesis rightwards arrow F left parenthesis y right parenthesis logical and P left parenthesis x comma y right parenthesis     2.     there exists x for all y space S left parenthesis x right parenthesis logical and left parenthesis F left parenthesis y right parenthesis rightwards arrow P left parenthesis x comma y right parenthesis right parenthesis     3.     there exists x for all y space S

Q: 2. In the following wff, identify (i) the main operator, (ii) all of the free variable occurrences,…

A: Main operator: If the sentence has only one logic, then it is the main operator of the sentence.…

Q: 2. For each of the following relations on the set {1,3,4, 7}. • R1 = {(7, 7), (1, 1), (4, 4), (3,…

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Q: 1. The following subsets A, B, and C of R XR are relations on R. Sketch the set. (i) B = {(x, y):…

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Q: If 'I' denotes the 'divides' relation, then what can be said about 'b' if (2 | b) ^ (b | 2) (2…

A: there are two relations 2 is divisible by b and b is divisible by 2 and there is a disjunction(means…

Q: Suppose a and b are positive integers and 2021 α 2022 2022 b 2023 If s is the minimum value of a+b,…

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Q: Let A be the first-order logic formula \x³y²(x, ƒ(v), a), where P is a relation symbol, ƒ is a…

A: Given first order logic formula∀ x∃yP(x,f(y),a)Where,P = Relation symbolf = function symbola =…

Q: 6. Suppose that inf A > inf B. a. Show that there exists a € B such that a is a lower bound of A. b.…

A: 6a) Given: Two sets A and B such that infA>infB, To Prove: there exists an element a∈B which is a…

Q: 21. Simplify the following Boolean expressions to a minimum number of literals using Karnaugh maps.…

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Q: All discrete variables are categorical but not all categorical variables are discrete. True False

A: A variable is a characteristic that is being measured.

Q: Let A = {x € Rx > 5 and x 15 and x 8 and x < 12

A: Given:- A=x∈R|x≥5 and x&lt;18 B=x∈R|x≥15 and x≤22 C=x∈R|x&gt;8 and x&lt;12

Q: Define a relation D on the set of real of numbers as follows: Vx, y ≤ R, x Dy x-y is irrational OD…

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Q: Let a₁ = -3 h -2 a₂ = -6 1 , and a3 = -8 20 The set {a₁, a2, a3}| will span R³ unless h = 19 (If…

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Q: Let S1= {1, 5, 10, 15, 20} and let S2 = {1, 2, 3, 4, 5}. What is: (a) S1 ∪ S2 (b) S1 ∩ S2 (c) S1 –…

A: Given: The given sets are S1=1, 5, 10, 15, 20 and S2=1, 2, 3, 4, 5. To find: The main aim is to find…

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

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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: In this group of problems, you are given two statements, A and B: determine whether one statement…

A: Solution

Q: 8. Show that the set (0, 1) – {1/2, 1/3, 1/4, -..} is uncountable.

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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: Consider the relations given below: xRy:x loves y xRy:x2y iii. xRy:x is in the same classroom with y…

A: If x = y and y = x then we can say that relation is symmetric relation.

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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Q: Technical Question: Which of the following best characterizes the statements, where A and B are any…

A: Two statements are given as, A : fx = x2+x logzx is Ox3 B : fx = x logxx is Ωx2 logx where A and B…

Q: 7. (Relations) Consider the set A= (1,2, 3, 4, 5), and a relation R defined by zRy -y is an integor…

A: Given, A = 1, 2, 3, 4, 5xRy ⇔x2-y is an integer multiple of 3.

Q: The counterexample of A = {1} and B = Ø disproves which of the following statements where P(X)…

A: Given that A=1,B=∅. For (a). PA∩B=P1,∅∩∅=P∅=∅ And, P(A)∩P(B)=P1∩P(∅)=1,∅∩∅=∅ Hence statement of (a)…

Q: (4) Let X and Y be sets. Select which one of the following statements is equivalent to the statement…

A: It is given that PX∪Y×Y⊆PX×X∪Y where X and Y are sets. Here P(X) denotes the power set of X. We know…

Q: Q3. Suppose A = {1,2,3,4}. Which of the following sets is the relation R = {(a,b)|a+b is odd }? A. R…

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Q: 9.4. Let A = {a, b, c} and B = {1,2,3,4}. Then R1 = {(a, 2) , (a, 3) , (b, 1),(b,3), (c, 4)} is a…

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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: 2. Let A, B and C be sets, and let g: A → B and f: B → C be functions. Prove: (i) If f, g are…

A: Answer given below.

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: 4. Let A = {a,b), B = {1,2], and C= {1,2,3), and see Definitions 2.2.4 and 2.2.7. (a) List the…

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Q: (i) If A and B are two sets such that ACB, then m* (A) ≤m* (B).

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Q: a Are ALL the following three pairs in the relation R: (4.2) (1,2) (5,1) b Is 4 a minimum element?…

A: R=4,21,2,5,1a. (1,2) is not the element of R because from Hass diagram 2 is related to 1    here…

Q: Choose the relations that are a functions A) B) D) 21- {(0, 18), (1, 14), (2, 10), (2, 6), (3, 9)}…

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Q: the lollowing relationships lincar or nonlinear? Explain. (w) The bowling place in under new…

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Q: Consider the following statements: T(x, y): "x eats y". A(x): "x is wise". S(x): "x is hungry".…

A: option 5 is correct

Q: each part below, indicate (by making suitable arguments) whether the following sets are open…

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