Questions
"If it is a good watch then it is a Titan watch. It is a Titan watch, therefore, it is a good watch". This argument is _____________.
- valid
- invalid
- may be valid or invalid
- invalid if conditional connective is replaced by biconditional connective
- True
- False
State whether the statement
P: "if x is a real number such that $x^3+2x=0$, then $x$ is $0$" is true/false.
- True
- False
Check the validity of the following statement:
$p:100$ is a multiple of $4$ and $5$
- True
- False
Determine whether the argument used to check the validity of the following statement is correct.
$p:$ If $x^{2}$ is irrational, then $x$ is rational'
The statement is true because the number $x^{2}=\pi^{2}$ is irrational, therefore $x=\pi$ irrational.
- True
- False
Check the validity of the following statement:
$p:60$ is a multiple of $3$ and $5$
- True
- False
State whether the statement
$p:$ If $x$ is a real number such that $x^{3}+19x=0$ , then $x$ is $0$ is true / False
- True
- False
Check the validity of the following statement:
$p:125$ is a multiple of $5$ and $7$
- True
- False
Tell if the following statement is true or false. In case give a valid reason for saying so
$p:$ If $x$ and $y$ are integers such that $x>y$. then $-x<-y$.
- True
- False
If p and q are mathematical statements, then in order to show that the statement p and q is true, we need to show that:
- The statement p is true and the statement q is not true
- The statement p is false and the statement q is true.
- The statement p is true and the statement q is false
- The statement p is true and the statement q is true
The component statements are:
p: You are wet when it rains.
q: You are wet when you are in river.
The compound statement of these component statements using appropriate connective is:
- You are not wet when you are in river or it rains.
- You are wet when you are in river and it rains.
- You are wet when it rains and you are in a river
- You are wet when it rains or you are in a river.
Two pairs of statement are:
p: If a quadrilateral is a rectangle, then its opposite sides are equal.
q: If opposite sides of a quadrilateral are equal, then the quadrilateral is a rectangle.
The combined statement of these pairs using If and only if is:
- A quadrilateral is a rectangle if and only if its all sides are equal.
- A quadrilateral is a rectangle if and only if its opposite sides are equal.
- A quadrilateral is a square if and only if its opposite sides are equal.
- A quadrilateral is not a rectangle if and only if its opposite sides are equal.
Name the technique used in the first step of the solution to the problem below :
Verify that 5 is irrational
Solution : Let us assume that 5 is rational
- Counter example
- Direct method
- By Contradiction
- Contrapositive method
Name the technique used in the solution of the problems below :
Question: Show that the following statement is false: If n is an odd integer, then n is prime.
Solution: The given statement is in the form “if p then q” we have to show that this is false, If p then ~q.
If n= 99 is odd integer which is not a prime number. Thus, we conclude that the given statement is false.
- Counter example
- Contrapositive method
- Direct method
- By Contradiction