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Which of these relations on the set of all people are equivalence relations? Determine the properties of an equivalence relation that the others lack.
2a) {(a, b) ∣ a and b are the same age}
2b) {(a, b) ∣ a and b speak a common language}
I.) Identify if the following statements are predicate logic. Give a domain of discourse for each propositional function.
- The movie won the Academy Award for the past 2 years.
- 1 + 3 = 4
- (x+2)2 is a prime number.
- man is mortal
- not all people are dishonest.
II.) Convert the given argument into four type of nested quantifier.
"Every Math Teacher is like by some students"
(note: you may take different types of approach in your sentences but the thought of the quantifiers must still be there)
Premises: If there was an Easter Concert at the National Arena, then parking was difficult. If they arrived on time, then parking was not difficult. They arrived on time.
Conclusion: There was no Easter Concert.
Determine whether the conclusion follows logically from the premises. Explain by representing the statements symbolically and using rules of inference.
Let proposition p be T and proposition q be F. Find the truth value of the following.
1. p ^ (¬p v q)
2. ¬p v p→q
3. p v ¬q→q
4. p→q↔p
p ^¬q (q→¬p)
Translate the gaming system requirement, , into English where the predicate S(x,y) is “x is in state y” and where the domain for x and y consists of all systems and all possible states, respectively.
What standard form of valid arguments is illustrated with the argument "If it is bright and sunny today, then I will wear my sunglasses. I will not wear my sunglasses. Therefore, it is not bright and sunny today."?
What standard form of valid arguments is illustrated with the argument "If it is bright and sunny today, then I will wear my sunglasses. I will not wear my sunglasses. Therefore, it is not bright and sunny today."?
Express this gaming system requirement using predicates, quantifiers, and logical connectives: “When there are less than 2 gigabytes of available RAM, an error message is displayed.”
Let the set U = {1, 2, 3, 4, 5}, be the universe. Let Y = {(n+2)| n = 2, 3} 5 and X = {3, 4}. Write the following sets using set builder notation
Let x, y ∈ R. Determine the truth value of the following statements. Give 5 an example, if true; give a counterexample, if false.
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