CH5-Predicates and Quantifiers

What is the correct negation of the statement 'All students passed the exam'?

• Every student passed the exam

• All students did not pass the exam

• No student passed the exam

• Some students did not pass the exam

Answer explanation

The correct negation of 'All workers got bonus' is 'Some worker did not get bonus', as it implies that not all workers received a bonus.

What is the correct negation of the proposition: ∃y∃x(x-y≠0)?

• ∀y∀x(x-y=0)

• ∃y∃x(x-y≠0)

• ∀y∃x(x-y<0)

• ∃y∃∀x(x-y>0)

Answer explanation

The correct negation of ∃y∃x(x-y≠0) is ∃y∃x(x-y=0), where the inequality is changed to an equality sign to negate the proposition.

What is the correct interpretation of the proposition: ∀z∀y∃x(xyz=0)?

• For all y, there exists x such that there exists z, xyz is equal to 0

• For all z, there exists x such that there exists y, xyz is equal to 0

• For all z, there exists x such that for all y, xyz is different to 0

• For all z, there exists x such that for all y, xyz is equal to 0

Answer explanation

For all z, there exists x such that for all y, xyz is equal to 0

What is the correct negation of the statement 'Some students passed the exam'?

• No student passed the exam

• Some students did not pass the exam

• All students passed the exam

• Every student passed the exam

Answer explanation

The correct negation of 'Some worker got bonus' is 'No worker got bonus' as it implies that there are no workers who received a bonus.

What is the correct negation of the statement: There exists a pair of students Nour and Lina such that Nour's score is equal to Lina's score?

• There exists a pair of students Nour and Lina such that Nour's score is equal to Lina's score

• There exists a pair of students Nour and Lina such that Nour's score is not equal to Lina's score

• There exists a pair of students Nour and Lina such that Nour's score is less than Lina's score

• There exists a pair of students Nour and Lina such that Nour's score is greater than Lina's score

Answer explanation

Choose the negation where the equation is not equal to zero, which is ∃y∃x(x-y≠0)

What is the correct negation of the statement 'All students passed the exam'?

• No student passed the exam

• Every student passed the exam

• Some student did not pass the exam

• All students did not pass the exam

Answer explanation

The correct negation of 'All workers got bonus' is 'Some worker did not get bonus' as it allows for the possibility that not all workers received a bonus.

What is the correct interpretation of the proposition: ∀ Lina ∃Mariem ∃Emna( Lina+Mariem>Emna)

• There exists Lina, Mariem, and Emna such that Lina+Mariem is greater than Emna

• For all Lina, there exists Mariem and Emna such that Lina+Mariem is greater than Emna

• For all Lina, there exists Mariem such that Lina+Mariem is greater than Emna

• There exists Lina, Mariem such that Lina+Mariem is greater than Emna

Answer explanation

For all x, there exists y and z such that x+y is greater than z