2.5
7.In a survey of college​ students, each of the following wasfound. 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 tabletand 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 exactlytwo of these​ devices?
​(Simplify your​ answer.)
​e) Of the college students​ surveyed, how many owned at leastone of these​ devices?
​(Simplify your​ answer.)
4.
Thirty-five cities were researched to determine whether they hada 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 professionalsports​ team?
​(Simplify your​ answer.)
​b) How many of the cities surveyed had a professional sportsteam and a​ symphony, but not a​ children's museum?
​(Simplify your​ answer.)
​c) How many of the cities surveyed had a professional sportsteam or a​ symphony
​(Simplify your​ answer.)
​d) How many of the cities surveyed had a professional sportsteam 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 logicalor 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 logicalor r(p ∨ ~q) ∨ r.
9.
Determine the symbolic form of the compound statement andconstruct 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 logicalor tilde p(t ∧ ~s) ∨ ~p
and
left parenthesis s logical and tilde p right parenthesis logicalor 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 andeach term can be T or F regardless of which letter is being used orwhether it is negated or not.
B.
​Yes, because the second expression contains the same threevariables as the first expression.
C.
​No, the truth table for the first expression has 5 trues andthe truth table for the second expression only has 3 trues.
D.
​No, because there is no relationship between the firstexpression and the second expression.
E.
​Yes, because half the answers for each expression will be trueand half will be false.
