2. Let 𝑛∈Z ^+ and consider the following relations 𝑅⊆R×R and 𝐸⊆Z×Z: 𝑥𝑅𝑦 ⇔ 𝑥 − 𝑦 ∉ Q 𝑎𝐸𝑏 ⇔ 𝑛|𝑎 − 𝑏 [3 pts] Prove in pros

[answerhappygod]

2. Let 𝑛∈Z ^+ and consider the following relations 𝑅⊆R×R and𝐸⊆Z×Z:
𝑥𝑅𝑦 ⇔ 𝑥 − 𝑦 ∉ Q
𝑎𝐸𝑏 ⇔ 𝑛|𝑎 − 𝑏
[3 pts] Prove in prose that 𝑅 is not an equivalencerelation.
[8 pts] Prove in prose that 𝐸 is an equivalence relation.
3. [4 pts] The relations 𝐸 iscongruence mod 𝑛, for which modular arithmetic is well defined.Compute the sum, difference, and product of 12 and 18 mod 25.