Tag: proofs in mathematics

"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 $7$