Let the following predicates be given. Assume the domain for x consists of all the tools.
F(x) = x is used frequently
C(x) = x is in the correct place
E(x) = x is in excellent condition
Express each of the following English sentences in terms of F(x), C(x), E(x), quantifiers, and logical connectives.
1. There is a tool that is used frequently and is in excellent condition.
2. Some tools are neither in the correct places nor are used frequently.
3. No tools are in the correct places.
4. Every frequently used tool is not in excellent condition
Let the following predicates be given. Assume the domain for x consists of all the tools....
Let B(x), W(x), and S(x) be the predicates B(x): x is a female W(x): x is a good athlete S(x): x is young Express each of the following English sentences in terms of B(x), W(x), S(x), quantifiers, and logical connectives. Assume the domain is the set of all people. a) All good athletes are not young. b) A person is a good athlete only if it is the case that both she is a female and she is young. c)...
Let F(x, y) be the statement "x can fool y" where the domain consists of all people in the world Use quantifiers to express each of these statements.
Let the predicates P,T, and E be defined below. The domain is the set of all positive integers. P(x): x is odd T(x, y): 2x < y E(x, y, z): xy - z Indicate whether each logical expression is a proposition. If the expression is a proposition, then give its true value and show your work. If the expression is not a proposition, explain why no. 1(a) P(5) 1(b) ¬P(x) 1(c) T(5, 32) 1(d) ¬P(3) V ¬T(5, 32) 1(e) T(5,10)...
3. Suppose that the domain for x consists of all English text. P(x):“x is a clear explanation,” Q(x): “x is satisfactory,” and R(x):“x is an excuse,” Express each of these statements using quantifiers, logical connectives, and P (x), Q(x),and R(x). a) Some clear explanations are satisfactory b) All excuses are unsatisfactory c) Some excuses are not clear explanations. d) Does (c) follow from (a) and (b)? 4. Prove that if you pick four utensils from a drawer containing just spoons,...
In the following question, the domain of discourse is a set of employees who work at a company. Ingrid is one of the employees at the company. Define the following predicates: • S(x): x was sick yesterday • W(x): x went to work yesterday • V(x): x was on vacation yesterday Translate the following English statements into a logical expression with the same meaning. (c) Everyone who was sick yesterday did not go to work. (d) Yesterday someone was sick...
kindly solve it and show all the work here as i think its not
too difficult do it as soon as possible
11. (5 points) Given a quantified statement VxP(x) for some domain of x. Suppose you believe that statement is incorrect. How do you prove it? Explain 12. (5 points) Let S(x) be the predicate "x is a student", F(x) the predicate "x is a faculty member" and A(x, y) predicate "r has askedy a question" where the domain...
Express each of the following using quantified state- ments over the domain S of all college students and the predicates C(x) meaning "x is a computer science major," and D(x) meaning "x takes discrete mathemat- ics." Which statements are equivalent to one another? Which statements are negations of one another? (d) Not every computer science major takes discrete mathematics. (f) You must take discrete mathematics if you are a computer science major (g) Some computer science majors do not take...
Stuck on part f
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Please answer the following questions with solution, thanks
4. Consider the function f(x) = 2x + 1, a) Find the ordered pair (4. f(4) on the function. b) Find the ordered pair on the inverse relation that corresponds to the ordered pair from part a). c) Find the domain and range of f. d) Find the domain and the range of the inverse relation off. e) Is the inverse relation a function? Explain. 5. Repeat question 4 for the function...