MathDB
Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1966 AMC 12/AHSME
20
Negation of a Proposition
Negation of a Proposition
Source:
March 22, 2006
Problem Statement
The negation of the proposition "For all pairs of real numbers
a
a
a
,
b
b
b
, if
a
=
0
a=0
a
=
0
, then
a
b
=
0
ab=0
ab
=
0
" is: There are real numbers
a
,
b
a,b
a
,
b
such that
(A)
a
≠
0
,
a
b
≠
0
(B)
a
≠
0
,
a
b
=
0
(C)
a
=
0
,
a
b
≠
0
\text{(A)} \ a\ne0,ab\ne 0 ~~\text{(B)} \ a\ne 0, ab=0 ~~ \text{(C)} \ a=0,ab\ne 0
(A)
a
=
0
,
ab
=
0
(B)
a
=
0
,
ab
=
0
(C)
a
=
0
,
ab
=
0
(D)
a
b
≠
0
,
a
≠
0
(E)
a
b
=
0
,
a
≠
0
\text{(D)} \ ab\ne0,a\ne0 ~~\text{(E)} \ ab=0,a\ne0
(D)
ab
=
0
,
a
=
0
(E)
ab
=
0
,
a
=
0
Back to Problems
View on AoPS