2 Translating English Sentences into Formulas Consider the following two predicates: S(x) : x is a student in CSE015; M(x) : x plays a musical instrument. Let the domain be the set of all people. Using the above predicates, translate the following sentences into formulas using the appropriate quantifiers and operators. a) Not every student in CSE015 plays a musical instrument. b) A person is either a student in CSE015 or plays a musical instrument, but not both. c) There exists at least one student in CSE015 who does not play a musical instrument.

Determine if each statement below is true or false, and explain your reasoning.a) If two statements are logically equivalent, then so are their negations. b) If the statement p is a contradiction, then, for any statement q , the statement p -> q is a tautology. c) State the type of relation the statement, x2 = xy is? Discuss your answer.

a. Construct an interpretation (i.e., give the domain and the meaning of P(x)) in which (∀x)P(x) has the value true.b. Construct an interpretation in which (∀x)P(x) has the value false.c. Can you find one interpretation in which both (∀x)P(x) is true and (∃x)P(x) is false?d. Can you find one interpretation in which both (∀x)P(x) is false and (∃x)P(x) is true?

How do i solve these

Evaluate each expression

The stem-and-leaf display below gives the number of minutes that customers waited for their orders at two different restaurants. There were 14 wait times recorded for the first restaurant and 21 recorded for the second. Use the display to answer the questions that follow. Number of minutes customers waited First restaurant Second restaurant 9 05 89 751 144 55 7 88 77300 20 4 555 6 9533 2 3 1 3 5 6 4 7 Key: 9 + 9| 0 |5 - 5 (a) What were the ranges of wait times for the two restaurants? First restaurant Second restaurant (b) Which restaurant had the greater median wait time? OFirst restaurant Second restaurant OThe medians were the same (c) Which restaurant had more wait times from 40 to 49 minutes? OFirst restaurant OSecond restaurant OEach had the same

Kindly help explain this for me. Thank you.

Given the following definitions, write the following sentences using symbols. PCC=school name Let S = the set of students at PCC Let M(x) Let F(x) = x is enrolled full time = x is enrolled in a math class a) All PCC students are enrolled in a math class. b) Some PCC student is not enrolled in a math class. c) There is an PCC student that is enrolled in a math class or enrolled full time. d) For all PCC students, if a student is not enrolled full time then a student is enrolled in a math class.

Explain each step, excluding those that are labeled as “no justification needed.” For each step, identify the property of the real numbers being used and explain how that property is being applied.   I attached a picture of the step I need help with, along with the properties.

Which of the expressions below is being represented by this Venn diagram? A В Select one: O none of these options (C\(((A)) \ ((B)))) ((((B) n (T))) n A) (Cn ((((B))U A)))