To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free)
Top

Equivalence Statement

Logical Equivalence in simple word is the comparision of two logical statements. Meaning of the word logic is analysis. Analysis may be granted result or mathematical proof. Two statemnets satisfies the equivalance if the resultant truth table of both the given statements are exactly same. That is, the resultant truth values are the same. Equivalence statements satisfies the "if and only if" or biconditional operations. If A and B are two equivalant statements then one can be proved from another.

Symbol of Equivalence

We use '`-=` symbol to represent the term logical equivalence in discrete mathematics. Let us see about logical equivalence in this article.

Related Calculators
Calculator for Equivalent Fractions Equivalent Expression Calculator
Equivalent Ratio Calculator Equivalent Resistance Calculator
 

Logical Equivalence Table

Back to Top

If the last column of two given components in the logical equivalence table are the same, then the two components are said to be logical equivalent.

We can use'`-=` ' symbol to represent logical equivalences. Other name of logical equivalence is simple equivalence. These are the logical equivalence laws.

Logical Equivalence Examples

Back to Top

Given below are some of the logical equivalence examples:

Example 1: Show ~ (X`vv` Y) = (~X)`^^` (~Y) simple equivalence.

Proof:

LHS:

~ (X`vv` Y)

XYX`vv` Y
~ (X`vv` Y)
TTTF
TFTF
FTTF
FFFT

RHS:

(~X)`^^` (~Y)

XY~X~Y(~X)`^^` (~Y)
TTFFF
TFFTF
FTTFF
FFTTT

Last column of LHS table is equal to last column of RHS table. And so, it is a simple equivalence.

Example 2: Show (X`^^` Y) = ~ ((~X)`vv` (~Y)) simple equivalence.

Proof:

LHS:

(X`^^` Y)

XY(X`^^` Y)
TTT
TFF
FTF
FFF

RHS:

~ ((~X)`vv` (~Y))

XY~X~Y ((~X)`vv` (~Y))~ ((~X)`vv` (~Y))
TTFFFT
TFFTTF
FTTFTF
FFTTTF

Last column of LHS table is equal to last column of RHS table. And so, it is a simple equivalence.

Example 3: Show (X`vv` Y)`vv` (~(X`vv` Y)) =(X`vv` (~Y))`vv` Y simple equivalence.

Proof:

LHS:

(X`vv` Y)`vv` (~(X`vv` Y))

XYX`vv` Y
(~(X`vv` Y)(X`vv` Y)`vv` (~(X`vv` Y))
TTTFT
TFTFT
FTTFT
FFFTT

RHS:

(X`vv` (~Y))`vv` Y

XY~Y(X`vv` (~Y))(X`vv` (~Y))`vv` Y
TTFTT
TFTTT
FTFFT
FFTTT

Last column of LHS table is equal to last column of RHS table. And so, it is a simple equivalence.

Related Topics
Math Help Online Online Math Tutor
*AP and SAT are registered trademarks of the College Board.