Testing Injectivity and Surjectivity

Discrete Math · Axiom Academy

EXAMPLE Testing Injectivity and Surjectivity Determine if a function is one-to-one, onto, or bijective through visual analysis Excellent work! You've learned how to test functions for injectivity and surjectivity. Remember: Injective (One-to-One): Each element in the domain maps to a unique element in the codomain. No two arrows point to the same target. Surjective (Onto): Every element in the codomain is mapped to by at least one element from the domain. No element is left unmapped. Bijective: A function that is both injective AND surjective. Creates a perfect one-to-one correspondence between domain and codomain. Visual Test: Arrow diagrams make it easy to spot violations - look for duplicate targets (not injective) or unmapped elements (not surjective). These properties are fundamental in discrete mathematics and have important applications in cryptography, data structures, and algorithm design. Practice with different function mappings to strengthen your understanding!

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