Difference between revisions of "1971 AHSME Problems/Problem 6"
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\textbf{(B) }\ast\text{ is associative over }S\qquad \\ | \textbf{(B) }\ast\text{ is associative over }S\qquad \\ | ||
\textbf{(C) }\frac{1}{2}\text{ is an identity element for }\ast\text{ in }S\qquad | \textbf{(C) }\frac{1}{2}\text{ is an identity element for }\ast\text{ in }S\qquad | ||
− | \textbf{(D) }\text{Every element of }S\text{ has an inverse for }\ast\qquad | + | \textbf{(D) }\text{Every element of }S\text{ has an inverse for }\ast\qquad \\ |
\textbf{(E) }\dfrac{1}{2a}\text{ is an inverse for }\ast\text{ of the element }a\text{ of }S </math> | \textbf{(E) }\dfrac{1}{2a}\text{ is an inverse for }\ast\text{ of the element }a\text{ of }S </math> | ||
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Since the identity is <math>\frac{1}{2}</math>, not 1, we can see that statement E is false. | Since the identity is <math>\frac{1}{2}</math>, not 1, we can see that statement E is false. | ||
− | + | Hence, the answer is <math>\boxed{\textbf{(E)}}</math>. | |
-edited by coolmath34 | -edited by coolmath34 | ||
-fixed by DoctorSeventeen | -fixed by DoctorSeventeen | ||
+ | |||
+ | == See Also == | ||
+ | {{AHSME 35p box|year=1971|num-b=5|num-a=7}} | ||
+ | {{MAA Notice}} |
Latest revision as of 10:51, 1 August 2024
Problem
Let be the symbol denoting the binary operation on the set
of all non-zero real numbers as follows:
For any two numbers
and
of
,
. Then the one of the following statements which is not true, is
Solution
Statement A is true.
Statement B is true.
Statement C is true.
Statement D is true.
Since the identity is , not 1, we can see that statement E is false.
Hence, the answer is .
-edited by coolmath34 -fixed by DoctorSeventeen
See Also
1971 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.