Homework Statement
Identify the following as a valid or an invalid argument.
p → q
q ∧ r
--------------
∴ ~r → ~p
Homework Equations
N/A
The Attempt at a Solution
Truth table values:
(a) p → q TTFFTTTT
(b) q ∧ r TFFFTFFF
(c) a ∧ b TFFFTFFF
(d) ~r → ~p TFTFTTTT
(e) c → d...
Homework Statement
Using only NOT and XOR, construct a compound statement having the same truth table as:
(a) p OR q
(b) p AND q
Homework Equations
XOR is "exclusive OR." p XOR q = (p OR q) AND NOT (p AND q).
I have been working under the assumption that I can use parentheses.
The...
Thanks, jbunniii, for the hint. As you can see, my algebra is a bit rusty. This is what I came up with after your hint.
To prove that |a + b| ≤ |a| + |b|, we will first attempt to prove that (|a + b|)2 ≤ (|a| + |b|)2.
Since (|a + b|)2 is equal to (a + b)2, we have
a2 + b2 + 2ab ≤ (|a| +...
Homework Statement
Prove that |a + b| ≤ |a| + |b|.
Homework Equations
|a| = √a2
The Attempt at a Solution
Since |a| = √a2, then
|a + b| = √(a + b)2 = √(a2 + 2ab + b2) = √a2 + √b2 + √(2ab) = |a| + |b| + √(2ab).
And since the square root of a negative number is not defined...