Question

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.)

4.

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,

88

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

66

had a symphony and a​ children's museum, and

44

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

7.

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

8.

Construct the truth table for the compound statement

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

9.

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.

A.

​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.

B.

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

C.

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

D.

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

E.

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

Answer 1

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

Drawn Venn Diagram to make you understand the question easily