Logic and sets

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.

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.

9000086605

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

9000086606

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

9000086607

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

9000086608

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

1003034401

Level: 
C
There are \( 47 \) students in a class. Among these students \( 22 \) are members of a sports club, \( 33 \) are members of a film club and \( 20 \) students joined a literary club. Further, \( 17 \) students are members of the sports club and the film club, \( 13 \) joined the film club and the literary club, \( 6 \) attend the sports club and the literary club. Only one student is a member of all the clubs. How many students from the class attend neither the sports club nor the literary club?
\( 11 \)
\( 7 \)
\( 36 \)
\( 4 \)