Free CLAST Logical Reasoning Questions and Answers — Questions and Answers
Question 1: The statement "Bob is an engineer or Tom is a musician" is negated by:
- Bob is not an engineer and Tom is not a musician (Correct answer)
- Bob is an engineer and Tom is not a musician
- Bob is not an engineer or Tom is not a musician
- Bob is not an engineer and Tom is a musician
Correct answer: Bob is not an engineer and Tom is not a musician
According to De Morgan's Laws, the negation of a disjunction ('P or Q') is the conjunction of the negations ('not P and not Q'). Therefore, the negation of 'Bob is an engineer or Tom is a musician' is 'Bob is not an engineer and Tom is not a musician'.
Question 2: "Pam is going to work and Kay is going shopping," in the negative, means:
- Pam is going to work and Kay is not going shopping
- Pam is not going to work or Kay is going shopping
- Pam is not going to work or Kay is not going shopping (Correct answer)
- Pam is not going to work and Kay is not going shopping
Correct answer: Pam is not going to work or Kay is not going shopping
According to De Morgan's Laws, the negation of a conjunction ('P and Q') is the disjunction of the negations ('not P or not Q'). Therefore, the negation of 'Pam is going to work and Kay is going shopping' is 'Pam is not going to work or Kay is not going shopping'.
Question 3: If Kari is presented with a job offer, she will take it, the converse is true:
- If Kari is offered a job, she will not accept it
- If Kari is not offered a job, she will not accept it
- Kari is offered a job and she does not accept it (Correct answer)
- Kari is offered a job and she accepts it
Correct answer: Kari is offered a job and she does not accept it
The original statement is a conditional: 'If Kari is presented with a job offer (P), she will take it (Q)'. The condition under which this statement is false is when the premise (P) is true, but the conclusion (Q) is false. This means 'Kari is offered a job AND she does not accept it', which is the logical negation of the conditional statement.
Question 4: The opposite of "All the staff members will attend the picnic" is:
- All the employees will attend the picnic
- All the employees will not attend the picnic
- Some employees will not attend the picnic
- Some employees will attend the picnic (Correct answer)
Correct answer: Some employees will attend the picnic
The logical opposite (negation) of a universal affirmative statement ('All X are Y') is a particular negative statement ('Some X are not Y'). Therefore, the negation of 'All the staff members will attend the picnic' is 'Some employees will not attend the picnic'. Option D, 'Some employees will attend the picnic', is not the logical opposite as it can be true even if the original statement is false (e.g., if only half the staff attends).
Question 5: It is illogical to claim that both Frank and Ralph are students. The logical equivalent is:
- If Frank is not a student, Ralph is not a student
- Ralph is not a student and Frank is not a student
- If Ralph is not a student, Frank is not a student
- Frank is not a student or Ralph is not a student (Correct answer)
Correct answer: Frank is not a student or Ralph is not a student
The statement 'It is illogical to claim that both Frank and Ralph are students' means that the conjunction 'Frank is a student AND Ralph is a student' is false. According to De Morgan's Laws, the negation of 'P AND Q' is 'NOT P OR NOT Q'. Thus, the logical equivalent is 'Frank is not a student OR Ralph is not a student'.
Question 6: "If Joe moves back east, then he will feel homesick" has the following logical equivalent:
- Joe will get homesick, or he does not move back east (Correct answer)
- If Joe does not get homesick, then he moved back east
- Joe does not move back east or he does not get homesick
- Joe moves back east, or he does not get homesick
Correct answer: Joe will get homesick, or he does not move back east
A conditional statement 'If P, then Q' is logically equivalent to 'Not P or Q'. In this case, P is 'Joe moves back east' and Q is 'he will feel homesick'. Therefore, the equivalent statement is 'Joe does not move back east or he will feel homesick', which matches option A when the clauses are reordered.
Question 7: If Mary has a son, then, logically, she is a mother, hence the sentence is equivalent to:
- If Mary is not a mother, then she does not have a son (Correct answer)
- Mary has a son or she is a mother
- If Mary is a mother, then she has a son
- If Mary does not have a son, then she is not a mother
Correct answer: If Mary is not a mother, then she does not have a son
The original statement is a conditional: 'If Mary has a son (P), then she is a mother (Q)'. The contrapositive of a conditional statement is logically equivalent to the original statement. The contrapositive is formed by negating both parts and reversing the order: 'If not Q, then not P'. Thus, the equivalent is 'If Mary is not a mother, then she does not have a son'.
Free CLAST Logical Reasoning Questions and Answers
The statement "Bob is an engineer or Tom is a musician" is negated by: