Answer: 8X2=8
Step-by-step explanation:
I can't conveniently copy the logical symbols you use, so I write
AND = ∧ (conjunction)
OR = ∨ (disjunction)
NOT = ¬
Tautologically,
p = (p AND q) OR (p AND NOT q)
and we can distribute the OR to get the equivalent statement
(p OR (p AND NOT q)) AND (q OR (p AND NOT q))
and again to get
((p OR p) AND (p OR NOT q)) AND ((p OR q) AND (q OR NOT q))
Now, q OR NOT q is always true, and p OR p is simply p, so we have
p = p AND (p OR q) AND (p OR NOT q)
This shows that p OR NOT q is already included in p, so our initial statement is simply
p AND (NOT p OR NOT q)
Distributing the conjunction, we get
(p AND NOT p) OR (p AND NOT q)
p AND NOT p is tautologically false, but we're considering a disjunction, so the truth value of p AND NOT q is the only value that's relevant. So, the initial statement collapses to
p AND NOT q
Answer:
The range is 3.
Step-by-step explanation: To find the range you have to subtract the largest data number from the smallest data number. The highest is 3 and the lowest is 2. 3-2 is 1.
Answer:
Step-by-step explanation:
As with any equation involving fractions, you can multiply the equation by the least common denominator to eliminate fractions. Then solve in the usual way.
c) 1/a +b = c
1 +ab = ac . . . . multiply by a
1 = ac -ab . . . . subtract ab
1 = a(c -b) . . . . . factor out a
1/(c -b) = a . . . . divide by the coefficient of a
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d) (a-b)/(b-a) = 1
a -b = b -a . . . . . multiply by b-a
2a = 2b . . . . . . . . add a+b
a = b . . . . . . . . . . divide by the coefficient of a
Please be aware that this makes the original equation become 0/0 = 1. This is why a=b is not an allowed condition for this equation. As written, it reduces to -1 = 1, which is false. One could say <em>there is no solution</em>.
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f) bc +ac = ab . . . . . multiply by abc
bc = ab -ac . . . . . . subtract ac
bc = a(b -c) . . . . . . factor out a
bc/(b -c) = a . . . . . . divide by the coefficient of a
