A and B are subsets of U, and A∩B, A∩B′, A′∩B, and A′∩B′ are
each nonempty....
A and B are subsets of U, and A∩B, A∩B′, A′∩B, and A′∩B′ are
each nonempty. Select ALL of the following which form partitions of
U.
A. A,B,A∩B
B. A∩B,A∩B′,B∩A′,A′∩B′
C. A∪B,A∩B
D. A,A′
E. A,B′
F. A∪B,A′∩B′
G. A,B∩A′,A′∩B′
H. B,A′
I. B,B′
J. A,B
(a) Show that if a, b ∈ R, then |a| ≤ |a − b| + |b|....
(a) Show that if a, b ∈ R, then |a| ≤ |a − b| + |b|.
(b) Deduce that if a, b ∈ R, then |a| − |b| ≤ |a − b|.
Verify that the vectors a, b, and a+b, and, respectively, a, b,
and a−b satisfy the...
Verify that the vectors a, b, and a+b, and, respectively, a, b,
and a−b satisfy the triangle inequality.
a=2i+j
b=i+3j
8. Let a, b be integers. (a) Prove or disprove: a|b ⇒ a ≤ b. (b)...
8. Let a, b be integers. (a) Prove or disprove: a|b ⇒ a ≤ b. (b)
Find a condition on a and/or b such that a|b ⇒ a ≤ b. Prove your
assertion! (c) Prove that if a, b are not both zero, and c is a
common divisor of a, b, then c ≤ gcd(a, b).