# property of equality

• December 6th 2010, 05:08 PM
jpmath2010
property of equality
state the property which is a reason for each statement.
a. if a<0 and b> 0, then a<b.
b. if x>7, then x is not equal to 7.
c. if 5>9 and 2<3, then 7<12.
d. if m = 10 and n= 6, then m+n = 6
e. if squareroot of a = 5 is true, then square root of a + 4 is false

a.transitive property
b.trichotomy property
c.subtraction property of equality
e. ?????

iF any could know the exact answer please check my work? thanks....
• December 6th 2010, 06:07 PM
Ackbeet
Are you sure you typed c and d and e correctly? Double-check those problem statements, if you would, please. Definitely agree with a and b's answers.
• December 7th 2010, 05:47 PM
jpmath2010
thank you sir for your time looking and checking my work. sir that is exactly the problem ,taken from the book of geometry ( Edwin E. Moise, Floyd L. Downs Jr.-Addison Wesley) page 27 problem set number 2. thank you sir for your effort..God bless
• December 7th 2010, 06:32 PM
bjhopper
Hi jpmath,
You need to correct c d and e as noted by Ackbeet. You are making typing errors

bjh
• December 7th 2010, 06:56 PM
Ackbeet

Well, assuming you're typing the problem statements correctly, here's what I would say:

c. This statement is what we call in logic "vacuously true". The if part is false (it is not true that 5>9), and hence you're allowed to conclude anything whatsoever. Now, if the problem statement is supposed to be this:

If 5<9 and 2<3, then 7<12 (the difference is the first inequality),

then I would say the additive property of inequalities is what works for you there.

d. This is quite simply not true in normal arithmetic. Now, if you're doing modular arithmetic, you might be able to say that. (modulo 10, for example, although then you wouldn't have m = 10, but m = 0). In normal arithmetic, if m = 10 and n =6, then m + n = 16, not 6.

e. This is a nonsensical statement. It simply doesn't parse mathematically. I suppose you could take the square root of an equation (a = 5), but then why would you compare that in a truth-functional sense with the square of something that's not an equation (a+4)? Did you mean this:

If $\sqrt{a}=5$ is true, then $\sqrt{a}=4$ is false?