Logic and sets

9000089002

Level: 
C
Students from a class decided to order books for forthcoming holiday. The book-shop in the neighborhood had two bestsellers on the stock: a crime novel and a horror stories. There were \(31\) students in the class in total. From this total, \(22\) students bought horror stories. Altogether \(12\) students bought just one of the books. Two students did not buy any of these books. How many students bought the crime novel?
\(24\)
\(7\)
\(5\)

9000089005

Level: 
C
There are two types of cheese in a shop. Altogether \(153\) customer were in the shop during a day. From this total, \(65\) customers bought the first cheese. From the same total, \(49\) customers bought the second cheese. \(20\%\) of customers which bought at least one of the types of cheese bought actually both types. How many customers did not buy any of these two cheeses?
\(58\)
\(39\)
\(19\)

9000089003

Level: 
C
Students from a class bought a snack in the school lunch-room. There were \(31\) students in the class in total. Altogether \(8\) students had snack from their home and they did not buy anything. Altogether \(12\) students bought hamburger and \(15\) students bought hot-dog. How many students bought both hamburger and hot-dog?
\(4\)
\(19\)
\(8\)

9000089007

Level: 
C
A class in the school has \(35\) students. On the last holiday the students visited Slovakia, Croatia and Bulgaria. From the total amount of \(35\), \(7\) students have been in Slovakia, \(7\) students have been in Croatia, \(5\) students have been in Bulgaria, \(21\) students have not been abroad, one student was in every of these countries, two students have been in both Bulgaria and Croatia but not in Slovakia, one student has been in both Bulgaria and Slovakia but not in Croatia. How many students visited either Slovakia or Croatia?
\(11\)
\(7\)
\(3\)

9000089001

Level: 
C
Students from a class have a possibility to work in mathematical and physical hobby groups. There are \(31\) students in the class. From the total, \(21\) students are members of mathematical group. Some of the students are members of both groups, but there are \(10\) which are members of just one group. There are \(3\) students which are not members of any of those groups. How many students are members of both mathematical and physical groups?
\(18\)
\(16\)
\(19\)

9000089006

Level: 
C
A questionnaire on popular singers has been filled by \(200\) girls from a high-school. The girls had to mark the singers from three most popular (Justin Timberlake, Justin Bieber and Axl Rose) which they like. Justin Timberlake got \(78\) votes, Justin Bieber got \(75\) votes and Axl Rose \(101\) votes. There were \(28\) girls which voted for all three singers. There were \(22\) girls which voted for two singers. One half of this amount are fans of the pair Bieber and Rose. The number of the girls which like only Justin Bieber is smaller by \(7\) comparing to the number of girls which like only Justin Timberlake. How many girls did not like any of these three singers?
\(24\)
\(32\)
\(11\)

9000086601

Level: 
B
Determine the truth values of propositions \(a\) and \(b\) if you know that the compound proposition \[ \neg (a \vee b) \] is true.
Both statements are false.
Both statements are true.
The statement \(a\) is true, \(b\) is false.
The statement \(a\) is false, \(b\) is true.

9000086602

Level: 
B
Determine the truth values of propositions \(a\) and \(b\) if you know that the compound proposition \[ \neg a \vee b \] is false.
The statement \(a\) is true, \(b\) is false.
Both statements are true.
The statement \(a\) is false, \(b\) is true.
Both statements are false.

9000086603

Level: 
A
Determine the truth values of propositions \(a\) and \(b\) if you know that the compound proposition \[ \neg a \wedge b \] is true.
The statement \(a\) is false, \(b\) is true.
Both statements are true.
The statement \(a\) is true, \(b\) is false.
Both statements are false.

9000086604

Level: 
B
Determine the truth values of propositions \(a\) and \(b\) if you know that the compound proposition \[ \neg (a \wedge \neg b) \] is false.
The statement \(a\) is true, \(b\) is false.
Both statements are true.
The statement \(a\) is false, \(b\) is true.
Both statements are false.