"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 _____________.

While simplifying $\sqrt { \frac { 1-cosx }{ 1+cosx }  } $, two students got the following two answers A & B.
A)  cosec x - cot x  (B)   $\frac { 1 }{ cosecx+cotx } $ What can you say about answers ?

State whether the statement
P: "if x is a real number such that $x^3+2x=0$, then $x$ is $0$" is true/false.

Choose the incorrect statements

Check the validity of the following statement:
$p:100$ is a multiple of $4$ and $5$

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.

Check the validity of the following statement:
$p:60$ is a multiple of $3$ and $5$

State whether the statement
$p:$ If $x$ is a real number such that $x^{3}+19x=0$ , then $x$ is $0$ is true / False

Check the validity of the following statement:
$p:125$ is a multiple of $5$ and $7$

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 $-x<-y$.

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 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:

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:

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

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.