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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?
- − (correct)
- √
- + (correct)
- × (correct)
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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