Mathematical language, notation and argument Quiz

1. Which symbol means 'if and only if'?

• A. $\Rightarrow$
• B. $\Leftarrow$
• C. $\Leftrightarrow$
• D. $\equiv$

2. $A=\{1,2,3,4\}$ and $B=\{3,4,5\}$. Find $A\cap B$.

• A. $\{1,2,3,4,5\}$
• B. $\{3,4\}$
• C. $\{1,2\}$
• D. $\emptyset$

3. Which of these is an identity?

• A. $x^2=4$
• B. $2x+1=7$
• C. $x^2-1=0$
• D. $(x+1)^2\equiv x^2+2x+1$

4. What is the largest set of real numbers that can be the domain of $f(x)=\frac{1}{x-2}$?

• A. $x\in\mathbb{R},x\ne2$
• B. $x>2$
• C. $x\ge0$
• D. $x\in\mathbb{R}$

5. Which statement about $x=2\Rightarrow x^2=4$ is correct?

• A. The converse is also true
• B. The converse is true and the original false
• C. The original is true but the converse is false, as $x$ could be $-2$
• D. Both are false