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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?