Question

If p is a rational number and q is an irrrational number

Is the number p/4 + q/5 rational or irrational and prove your answer.

Answer #1

Solved using basics of Real analysis.

If p is a rational # and q is an irrrational #
Is the number p/q rational or irrational and prove your
answer.

Prove that if p is a positive rational number, then √p + √2 is
irrational.

Prove the following: (By contradiction)
If p,q are rational numbers, with p<q, then there exists a
rational number x with p<x<q.

Let p and q be irrational numbers. Is p−q rational or
irrational?
Show all proof.

Prove by contradiction that 5√ 2 is an irrational number. (Hint:
Dividing a rational number by another rational number yields a
rational number.)

: Prove by contradiction that 5√ 2 is an irrational number.
(Hint: Dividing a rational number by another rational number yields
a rational number.)

10. (a) Prove by contradiction that the sum of an irrational
number and a rational number must be irrational. (b) Prove that if
x is irrational, then −x is irrational. (c) Disprove: The sum of
any two positive irrational numbers is irrational

1. Prove that the sum of any rational number with an irrational
number must be irrational.
2. Prove or disprove: If a,b, and c are integers such that
a|(bc), then a|b or a|c.

Irrational Numbers
(a) Prove that for every rational number µ > 0, there exists
an irrational number λ > 0 satisfying λ < µ.
(b) Prove that between every two distinct rational numbers there
is at least one irrational number. (Hint: You may find (a)
useful)

Prove that between any two rational numbers there is an
irrational number.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 11 minutes ago

asked 12 minutes ago

asked 13 minutes ago

asked 17 minutes ago

asked 17 minutes ago

asked 20 minutes ago

asked 26 minutes ago

asked 31 minutes ago

asked 36 minutes ago

asked 36 minutes ago

asked 42 minutes ago