Binary Operations PDF
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Prof. Rejie Vegas
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Summary
This document explains binary operations, providing examples and calculations. It defines binary operations, describes basic operations like addition, subtraction, multiplication, and division; and demonstrates how other binary operations can be defined, such as a * b = a + b - ab, a * b = 4a - b, and x⊕y = x² + 2y - xy.
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BINARY OPERATIONS Prof. Rejie Vegas Binary Operations A binary operation ∗ on a set of real numbers is an operation or a rule that combines two real numbers to produce another real number 𝒂 ∗ 𝒃 = 𝒄 → 𝒂, 𝒃, 𝒄 ∈ ℝ 𝟑+𝟐=𝟓 Basic binary operations 𝟔 − 𝟗 = −𝟑 +, −,×,÷ 𝟕×𝟏=𝟕...
BINARY OPERATIONS Prof. Rejie Vegas Binary Operations A binary operation ∗ on a set of real numbers is an operation or a rule that combines two real numbers to produce another real number 𝒂 ∗ 𝒃 = 𝒄 → 𝒂, 𝒃, 𝒄 ∈ ℝ 𝟑+𝟐=𝟓 Basic binary operations 𝟔 − 𝟗 = −𝟑 +, −,×,÷ 𝟕×𝟏=𝟕 Other binary operations 𝟖÷𝟒=𝟐 ∗, ⋆, ⨁ , ⊖ , ⊗ , ⊘ ,… Binary Operations Other binary operations can be defined as; 𝒂 ∗ 𝒃 = 𝒂 + 𝒃 − 𝒂𝒃 𝐸𝑣𝑎𝑙𝑢𝑎𝑡𝑒 𝟒 ∗ 𝟓 = 𝟒 + 𝟓 − (𝟒 × 𝟓) = 𝟗 − 𝟐𝟎 = −𝟏𝟏 Binary Operations Other binary operations can be defined as; 𝒂 ⋆ 𝒃 = 𝟒𝒂 − 𝒃 𝐸𝑣𝑎𝑙𝑢𝑎𝑡𝑒 𝟑 ⋆ 𝟐 = 𝟒(𝟑) − 𝟐 = 𝟏𝟐 − 𝟐 = 𝟏𝟎 Binary Operations Other binary operations can be defined as; 𝒙⨁𝒚 = 𝒙𝟐 + 𝟐𝒚 − 𝒙𝒚 𝐸𝑣𝑎𝑙𝑢𝑎𝑡𝑒 𝟓⨁𝟑 = 𝟓𝟐 + 𝟐(𝟑) − (𝟓 × 𝟑) = 𝟐𝟓 + 𝟔 − 𝟏𝟓 = 𝟑𝟏 − 𝟏𝟓 = 𝟏𝟔 Binary Operations TRY! 𝒂 ∗ 𝒃 = (𝒂 + 𝒃)(𝒂 − 𝒃) 𝐸𝑣𝑎𝑙𝑢𝑎𝑡𝑒 𝟐 ∗ −𝟑 = 𝟐 + −𝟑 [𝟐 − −𝟑 ] = (−𝟏)(𝟓) = −𝟓
