Give a proof by contradiction that given integers j and k wh

Give a proof by contradiction that given integers j and k where j 2 that j |kj |(k+1).

Solution

Proof by contradiction is type of proof but proved indirectly. Proof by contradiction is done in two ways one is in the

form of truth table in the given we are using truth tables.

let us assume that j,k are two integers.

condition is j>=2

it seem that j belongs to the gropu integers.

if the condition is and its negotiation is false then automatically the given condition is true.

j ^ k V j^ (k+1)

if the j is les than 2 or eqaul to means any n=number we consider for j upto fails the condiion.

Truth table of j ^ k

this j ^ k is true whne both are false and true only.

Truth table for =J ^ (k+1)

J ^k V J ^(K+1)

is

From the above truth tables result if the both cases are falase then the resultis false othre wise it irs true.

So the truth table what we get is true hence it is proved by contradiction.