Question

In: Advanced Math

2.5 7.In a survey of college students, each of the following was found. Of these students,...

2.5

7.In a survey of college students, each of the following was found. Of these students,

356356

owned a tablet,

294294

owned a laptop,

280280

owned a gaming system,

195195

owned a tablet and a laptop,

199199

owned a tablet and a gaming system,

137137

owned a laptop and a gaming system,

6868

owned a tablet, a laptop, and a gaming system, and

2626

owned none of these devices. Complete parts a) through e) below.

a) How many college students were surveyed?

(Simplify your answer.)

b) Of the college students surveyed, how many owned a tablet and a gaming system, but not a laptop?

(Simplify your answer.)

c) Of the college students surveyed, how many owned a laptop, but neither a tablet nor a gaming system?

(Simplify your answer.)

d) Of the college students surveyed, how many owned exactly two of these devices?

(Simplify your answer.)

e) Of the college students surveyed, how many owned at least one of these devices?

(Simplify your answer.)

Thirty-five cities were researched to determine whether they had a professional sports team, a symphony, or a children's museum. Of these cities,

1919

had a professional sports team,

1717

had a symphony,

1414

had a children's museum,

1111

had a professional sports team and a symphony,

had a professional sports team and a children's museum,

had a symphony and a children's museum, and

had all three activities. Complete parts a) through e) below.

a) How many of the cities surveyed had only a professional sports team?

(Simplify your answer.)

b) How many of the cities surveyed had a professional sports team and a symphony, but not a children's museum?

(Simplify your answer.)

c) How many of the cities surveyed had a professional sports team or a symphony

(Simplify your answer.)

d) How many of the cities surveyed had a professional sports team or a symphony, but not a children's museum?

(Simplify your answer.)

e) How many of the cities surveyed had exactly two of the activities?

(Simplify your answer.)

3.2

Construct the truth table for the compound statement q logical or left parenthesis p logical and tilde r right parenthesis .q ∨ (p ∧ ~r).

Construct the truth table for the compound statement

left parenthesis p logical or tilde q right parenthesis logical or r(p ∨ ~q) ∨ r.

Determine the symbolic form of the compound statement and construct a truth table for the symbolic expression. p ∨ (q ∨ r)

18.

Must the truth tables for

left parenthesis t logical and tilde s right parenthesis logical or tilde p(t ∧ ~s) ∨ ~p

and

left parenthesis s logical and tilde p right parenthesis logical or tilde t(s ∧ ~p) ∨ ~t

have the same number of trues in their answer columns?

Choose the correct answer below.

Yes, because the two expressions have exactly the same form and each term can be T or F regardless of which letter is being used or whether it is negated or not.

Yes, because the second expression contains the same three variables as the first expression.

No, the truth table for the first expression has 5 trues and the truth table for the second expression only has 3 trues.

No, because there is no relationship between the first expression and the second expression.

Yes, because half the answers for each expression will be true and half will be false.

Solutions

Expert Solution

Solved Q1) a, b, c, d, e

Drawn Venn Diagram to make you understand the question easily

Colby Messinger answered 1 year ago

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2.5 7.In a survey of college​ students, each of the following was found. Of these​ students,...

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2.5 7.In a survey of college students, each of the following was found. Of these students,...