6. Assume that the universal set is Z. Consider the following sentence:(t ≤ Z) (t • x = 20).(a) Explain why this sentence is an open sentence and not a statement.(b) If 5 is substituted for x, is the resulting sentence a statement? If it is astatement, is the statement true or false?(c) If 8 is substituted for x, is the resulting sentence a statement? If it is astatement, is the statement true or false?(d) If -2 is substituted for x, is the resulting sentence a statement? If it isa statement, is the statement true or false?

Here, in the question, it says, such that tx= 20.We know a statement in logic and mathematics is a…

Answered: Assume that the universal set is Z.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Please help me with the three questions (d,e,f) in the image below. Show all work. Thank you
ii. Let F(x,y) be the open sentence "x can fool y" where the domain of discourse is the set of all people in the world. Express each of these statements using logical quantifiers. c. Everybody can fool somebody. e. Everyone can be fooled by somebody. f. There is somebody who can be fooled by everybody.
Express this in predicate logic: Each email address has exactly one email box. M(x): x is an email address B(x,y): x has an email box y
For each of the statements below, write its converse and its contrapositive. (a) If A \ B = A, then AnB = 0. Converse: Contrapositive: (b) If P(A) CP(B) and BCC, then P(A) ≤ P(C). Converse: Contrapositive:
Create a truth table according to these specifications: There are 3 input bits, x2, x1, x0, and 2 output bits, s1, s0. The 2-bit output is the largest number of consecutive I's in the 3 input bits. (x2 is the most significant bit of the input, and s1 is the most significant bit of the output.) For example, input 000 gives output 00 (no 1’s), inputs 001 and 010 give output 01, input 011 gives output 10, etc. Show all 8 rows of the table clearly.
21. Let the following predicates be given. The domain is all computer science classes. I(r) = "x is interesting." U(x) = "x is useful." H(x, y) = “x is harder than y." M(x, y) = “x has more students than y." (a) Write the following statements in predicate logic. i. All interesting CS classes are useful. ii. There are some useful CS classes that are not interesting. iii. Every interesting CS class has more students than any non- interesting CS class. (b) Write the following predicate logic statement in everyday English. Don't just give a word-for-word translation; your sentence should make sense. (3)[I(x) A (Vy)(H(x,y)→ M(y, x))] (c) Formally negate the statement from part (b). Simplify your negation so that no quantifier lies within the scope of a negation. State which derivation rules you are using. (d) Give a translation of your negated statement in everyday English.
This proposition is a tautology: ((p→¬q)∧q)→¬p True or false I would appreciate step by step explanation
Any time you see A, B, or C in any of the quiz questions, those statement letters are true. Any time you see X, Y, or Z in any of the quiz questions, those statement letters are false. Not all letters, (A, B, C, X, Y, Z), will be in all statements. (-Av-C)v (X A) True False

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