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Mathematics for Economists
Chapter 1
Logic: Lectures
Statements and predicates
Mathematical implication
Compound statements and truth tables
Proofs
Logic: Problems
Problem: Necessary and sufficient conditions
Problem: Implications and converse
Problem: if, only if, and if and only if
Problem: Implication and equivalence with squares
Problem: Proof that squares are non-negative
Problem: Proof with squares and inequalities
Problem: Proof with square and zero
Problem: Proof with sum of squares
Problem: Proof, cubes can be negative
Problem: Proof, fourth powers cannot be negative
Problem: Proof with squares and strict inequalities
Problem: Proof that cubic function is injective
Sets: Lectures
Sets
Sets: Problems
Problem: Set member, subset, union, intersection and difference
Problem: Sets and logic
Problem: Subset, union, intersection and difference
Problem: Union, intersection, difference and complement
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Problem: Implication and equivalence with squares
Problem
Prove that
\[a=b⟹a^2=b^2\]
Prove that
\[a=b⟺a^2=b^2\]
Is false.
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Solution
