Math

Question Prove the statement "if 2x=32^{x} = 3, then xx is not rational" is logically equivalent to the original statement "if xx is rational, then 2x32^{x} \neq 3".

Studdy Solution

STEP 1

Assumptions
1. We are dealing with a statement and its contrapositive.
2. The original statement is "if xx is rational then 2x32^{x} \neq 3".
3. The contrapositive of a statement "if P then Q" is "if not Q then not P".
4. We need to formulate the contrapositive of the given statement.

STEP 2

Identify the original statement's components.
Let P be the statement "xx is rational" and Q be the statement "2x32^{x} \neq 3".

STEP 3

Formulate the contrapositive of the original statement using the components identified in STEP_2.
The contrapositive is "if not Q then not P".

STEP 4

Translate "not Q" and "not P" into mathematical terms based on the original statement.
"Not Q" translates to "2x=32^{x} = 3" and "not P" translates to "xx is not rational".

STEP 5

Combine the translations from STEP_4 to form the contrapositive statement.
The contrapositive statement is "if 2x=32^{x} = 3 then xx is not rational".
The contrapositive of "if xx is rational then 2x32^{x} \neq 3" is indeed "if 2x=32^{x}=3 then xx is not rational".

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord