Find the contrapositive of the following statement.
"If it is raining, then the soil is wet."
Given a conditional statement P\Rightarrow Q, the contrapositive is \sim Q \Rightarrow \sim P .
The given statement is:
"If it is raining, then the soil is wet."
Therefore the contrapositive is:
"If the soil is not wet, then it is not raining."
The contrapositive of this statement is: "If the soil is not wet, then it is not raining."
"If it's Sunday, then we don't work."
Given a conditional statement P\Rightarrow Q, the contrapositive is \sim Q \Rightarrow \sim P .
The given statement is:
"If it's Sunday, then we don't work."
Therefore the contrapositive is:
"If we work, then it's not Sunday."
The contrapositive of the statement is: "If we work, then it's not Sunday."
"If a number is not divisible by any other prime, then it is said to be a prime number."
Given a conditional statement P\Rightarrow Q, the contrapositive is \sim Q \Rightarrow \sim P .
The given statement is:
"If a number is not divisible by any other prime, then it is said to be a prime number."
Therefore the contrapositive is:
"If a number is not prime, then it divisible by a prime number."
The contrapositive of the statement is: "If a number is not prime, then it divisible by a prime number."
"If a number is divisible by 2, then it is even."
Given a conditional statement P\Rightarrow Q, the contrapositive is \sim Q \Rightarrow \sim P .
The given statement is:
"If a number is not divisible by any other prime, then it is said to be a prime number."
Therefore the contrapositive is:
"If a number is not prime, then it divisible by a prime number."
The contrapositive of the statement is: "If a number is not even, then it not divisible by 2".
"If a number is non-negative and non-positive, then it must be 0."
Given a conditional statement P\Rightarrow Q, the contrapositive is \sim Q \Rightarrow \sim P .
The given statement is:
"If a number is non-negative and non-positive, then it must be 0."
Therefore the contrapositive is:
"If a number is not zero, then it positive or negative."
The contrapositive of the statement is: "If a number is not zero, then it is positive or negative."
"If a positive number squared it is equal to itself, then the number must be 1."
Given a conditional statement P\Rightarrow Q, the contrapositive is \sim Q \Rightarrow \sim P .
The given statement is:
"Assume we have a positive number. If the number squared it is equal to itself, then the number must be 1."
Therefore the contrapositive is:
"Assuming we start with a positive number: If the number is not 1, then its square is not equal to itself."
The contrapositive of the statement is: "Assuming we start with a positive number: If the number is not 1, then its square is not equal to itself."
" If the determinant of a matrix is not zero, then it is invertible."
Given a conditional statement P\Rightarrow Q, the contrapositive is \sim Q \Rightarrow \sim P .
The given statement is:
"If the determinant of a matrix is non zero, then it is invertible."
Therefore the contrapositive is:
"If a matrix is not invertible, then its determinant is 0."
The contrapositive of the statement is: "If a matrix is not invertible, then its determinant is 0."