FREE CLAST Logical Reasoning Questions and Answers
The opposite of "All the staff members will attend the picnic" is:
The negation of the statement "All the employees will attend the picnic" is "It is not the case that all the employees will attend the picnic."
In symbolic logic, the negation can be represented as:
~(All the employees will attend the picnic)
This can be further simplified using quantifiers:
Some employees will attend the picnic
Therefore, the negation of the statement is "Some employees will attend the picnic."
The statement "Bob is an engineer or Tom is a musician" is negated by:
The negation of the statement "Bob is an engineer or Tom is a musician" is "It is not the case that Bob is an engineer or Tom is a musician."
In symbolic logic, the negation is often represented using the symbol "~" or "¬". Therefore, the negation can be written as:
~(Bob is an engineer or Tom is a musician)
This can be further simplified using De Morgan's laws:
~Bob is an engineer and ~Tom is a musician
So, the negation of the statement is "Bob is not an engineer and Tom is not a musician."
If Mary has a son, then, logically, she is a mother, hence the sentence is equivalent to:
The statement logically equivalent to "If Mary has a son, then she is a mother" is "If Mary is not a mother, then she does not have a son."
In symbolic logic, the original statement can be represented as:
Mary has a son -> Mary is a mother
By applying the contrapositive, the logical equivalence can be obtained:
Mary is not a mother -> Mary does not have a son
Therefore, the statement "If Mary is not a mother, then she does not have a son" is logically equivalent to the original statement.
It is illogical to claim that both Frank and Ralph are students. The logical equivalent is:
The statement logically equivalent to "It is not true that both Frank and Ralph are students" is "Frank is not a student or Ralph is not a student."
In symbolic logic, the original statement can be represented as:
~(Frank is a student and Ralph is a student)
By applying De Morgan's laws, the negation can be further simplified:
Frank is not a student or Ralph is not a student
Therefore, the statement "Frank is not a student or Ralph is not a student" is logically equivalent to the original statement.
"Pam is going to work and Kay is going shopping," in the negative, means:
The negation of the statement "Pam is going to work and Kay is going shopping" is "It is not the case that Pam is going to work and Kay is going shopping."
Using symbolic logic, the negation can be represented as:
~(Pam is going to work and Kay is going shopping)
By applying De Morgan's laws, the negation can be further simplified:
Pam is not going to work or Kay is not going shopping
Therefore, the negation of the statement is "Pam is not going to work or Kay is not going shopping."
If Kari is presented with a job offer, she will take it, the converse is true:
The negation of the statement "If Kari is offered a job, she will accept it" is "It is not the case that if Kari is offered a job, she will accept it."
Using symbolic logic, the negation can be represented as:
~(Kari is offered a job -> Kari will accept it)
By applying the negation to the implication, we get:
Kari is offered a job and Kari does not accept it
Therefore, the negation of the statement is "Kari is offered a job and she does not accept it."
"If Joe moves back east, then he will feel homesick" has the following logical equivalent:
The statement logically equivalent to "If Joe moves back east, then he will get homesick" is "Joe will get homesick, or he does not move back east."
In symbolic logic, the original statement can be represented as:
Joe moves back east -> Joe gets homesick
By applying the contrapositive, the logical equivalence can be obtained:
Joe does not get homesick -> Joe does not move back east
Therefore, the statement "Joe will get homesick, or he does not move back east" is logically equivalent to the original statement.