Tag: proofs in mathematics

Tell if the following statement is true or false. In case give a valid reason for saying so
$p:$ If $x$ and $y$ are integers such that $x>y$. then $-x<-y$.

If p and q are mathematical statements, then in order to show that the statement p and q is true, we need to show that:

The component statements are:

p: You are wet when it rains.

q: You are wet when you are in river.

The compound statement of these component statements using appropriate connective is:

Two pairs of statement are:
p: If a quadrilateral is a rectangle, then its opposite sides are equal.
q: If opposite sides of a quadrilateral are equal, then the quadrilateral is a rectangle.
The combined statement of these pairs using If and only if is:

Name the technique used in the first step of the solution to the problem below :
Verify that 5 is irrational
Solution : Let us assume that 5 is rational

Name the technique used in the solution of the problems below :

Question: Show that the following statement is false: If n is an odd integer, then n is prime.

Solution: The given statement is in the form “if p then q” we have to show that this is false, If p then ~q.

Without using truth , whether
$\left[ {p\Delta \left( { \sim q\Delta r} \right)} \right]V\left[ { \sim r\Delta  \sim q\Delta p} \right] \equiv p$

Solve it:-
$\left( {p \to q} \right) \to [\left( { \sim p \to q} \right) \to q]$

Which of the following is true

Let $p$ and $q$ be two propositions given by
$p$ : The sky is blue.
$q$ : The milk is white.
Then $p\wedge q$ will be