Logic and Sets

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.

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.

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.