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Questions and Answers
What is a binary operation?
What is a binary operation?
An operation that combines two real numbers to produce another real number.
Which of the following are basic binary operations?
Which of the following are basic binary operations?
Evaluate the binary operation 4 ∗ 5.
Evaluate the binary operation 4 ∗ 5.
-11
Evaluate the binary operation 3 ⋆ 2.
Evaluate the binary operation 3 ⋆ 2.
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Evaluate the binary operation 5 ⨁ 3.
Evaluate the binary operation 5 ⨁ 3.
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Evaluate the binary operation 2 ∗ -3.
Evaluate the binary operation 2 ∗ -3.
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Study Notes
Binary Operations Overview
- A binary operation combines two real numbers to produce another real number, expressed as ( a \ast b = c ), where ( a, b, c \in \mathbb{R} ).
- Basic operations include addition, subtraction, multiplication, and division.
- Example: ( 3 + 2 = 5 ), ( 6 - 9 = -3 ), ( 7 \times 1 = 7 ), ( 8 \div 4 = 2 ).
Alternative Binary Operations
- More complex binary operations can be defined with different rules.
- Example operation: ( a \ast b = a + b - ab ).
- For evaluation: ( 4 \ast 5 = 4 + 5 - (4 \times 5) = 9 - 20 = -11 ).
Another Defined Operation
- Another operation can be ( a \star b = 4a - b ).
- For evaluation: ( 3 \star 2 = 4(3) - 2 = 12 - 2 = 10 ).
Additional Operation Example
- An operation defined as ( x \oplus y = x^2 + 2y - xy ) can also be used.
- For evaluation: ( 5 \oplus 3 = 5^2 + 2(3) - (5 \times 3) = 25 + 6 - 15 = 31 - 15 = 16 ).
Trying an Operation
- An operation defined as ( a \ast b = (a + b)(a - b) ) can be evaluated.
- For example: ( 2 \ast -3 = (2 + -3)(2 - -3) = (-1)(5) = -5 ).
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Description
Test your understanding of binary operations on real numbers. This quiz covers the basic operations like addition, subtraction, multiplication, and division, as well as defining other binary operations. See how well you can evaluate these operations in different contexts.
