prime numbers

An unbiased six-faced dice whose faces are marked with numbers $1,2,3,4,5$, and 6 is rolled twice in succession and the number on the top face is recorded each time. The probabilit...

Let $p_1$ and $p_2$ denote two arbitrary prime numbers. Which one of the following statements is correct for all values of $p_1$ and $p_2$?

Let $p_1$ and $p_2$ denote two arbitrary prime numbers. Which one of the following statements is correct for all values of $p_1$ and $p_2$ ?

Consider the first order predicate formula φ: ∀x[(∀z z|x ⇒ ((z = x) ∨ (z = 1))) ⇒ ∃w (w > x) ∧ (∀z z|w ⇒ ((w = z) ∨ (z = 1)))] Here 'a|b' denotes that 'a divides b', where a and b...

Let $$p,q,r,s$$ represent the following propositions. $$p:\,\,\,x \in \left\{ {8,9,10,11,12} \right\}$$ $$q:\,\,\,x$$ is a composite number $$r:\,\,\,x$$ is a perfect square $$s:\,...

Which one of the following options is correct given three positive integers $$x, y$$ and $$z$$, and a predicate $$P\left( x \right) = \neg \left( {x = 1} \right) \wedge \forall y\l...

Suppose $$X$$ and $$Y$$ are sets and $$\left| X \right|$$ and $$\left| Y \right|$$ are their respective cardinalities. It is given that there are exactly 97 functions from $$X$$ to...