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To do this question you need to be really sure what the two symbols $\Rightarrow$ and $\Leftrightarrow$ mean.
$p\Rightarrow q$ essentially means that IF $p$ is True THEN $q$ is true.
$p\Leftrightarrow q$ means that $p$ is true if and only if $q$ is true.
This means that $p\Rightarrow q$ and $q\Rightarrow p$.
To get started, can you arrange these eight statements into two statements of the form $p\Rightarrow q$ and two statements of the form $p\Leftrightarrow q$? Once you have done this, have a look at the remaining eight statements from the problem.
$x> 4$ |
$x=-2 $ | $x> 1$ | $x^2+4x+4 =0$ |
$x^3> 1$ |
$x^2+x-2=0$ | $x> 2$ | $x=1$ |
A and B are two fixed points on a circle and RS is a variable diamater. What is the locus of the intersection P of AR and BS?
Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?