Final answer:
The difference between two consecutive square numbers is always an odd number, which is true. The displacement statements for both individuals in the question are false, as both have the same displacement. It's true that the Pythagorean theorem is used for vectors at right angles, true that waves with different frequencies can superimpose, and false that wave amplitudes only affect each other when precisely aligned.
Step-by-step explanation:
The difference between two consecutive square numbers is, in fact, an odd number. This statement is true. Considering two consecutive squares, namely n2 and (n+1)2, their difference is ((n+1)2 - n2) which simplifies to (2n + 1), clearly an odd number since it is the sum of twice an integer and 1.
Regarding the displacement question, the displacement of both individuals is the same since they both have traversed a distance of 2 blocks east and 5 blocks north, albeit in a different order. Therefore, the statement is false. Displacement is a vector quantity, and in both cases, it would be the hypotenuse of a right-angled triangle with sides 2 and 5.
For the Pythagorean theorem, it is true that we can use it to calculate the length of the resultant vector when two vectors are at right angles to each other. This is the essence of the Pythagorean theorem, which applies to right-angled triangles.
In probability, the complement of Event A, which is the outcome being an even number, would be all outcomes that are not even, meaning the odd numbers. Event A GIVEN B is asking for the probability of A (even numbers) given that B (outcomes less than four) has occurred. B GIVEN A is asking for the probability of B occurring given that A has occurred.
Superposition of waves with different frequencies is possible, making the statement true. They will interfere with each other while they pass through the same medium.
Lastly, the amplitude of a wave being affected by the amplitude of another wave depends on the phase relationship between the waves. If they are in phase (or out of phase), they can interfere constructively (or destructively), affecting the resultant amplitude. As such, precise alignment is not necessary for one wave's amplitude to affect another, which makes the statement false.