Reference no: EM132413925

Questions -

1. Define a relation ∼ on R² by stating that (a, b) ∼ (c, d) if and only if a² + b² ≤ c² + d². Show that ∼ is reflexive and transitive but not symmetric.

2. Show that an m x n matrix gives rise to a well-defined map from Rⁿ to R^m.

3. Find the error in the following argument by providing a counterexample. "The reflexive property is redundant in the axioms for an equivalence relation. If x ∼ y, then y ∼ x by the symmetric property. Using the transitive property, we can deduce that x ∼ x."