2. Let𝑛∈Z+andconsiderthefollowingrelations𝑅⊆R×Rand𝐸⊆Z×Z: 𝑥𝑅𝑦 ⇔ 𝑥 − 𝑦 ∉ Q 𝑎𝐸𝑏 ⇔ 𝑛|𝑎 − 𝑏 [3 pts] Prove in prose that 𝑅 is

[answerhappygod]

2. Let𝑛∈Z+andconsiderthefollowingrelations𝑅⊆R×Rand𝐸⊆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.
c. [4 pts] The relations 𝐸 is congruence mod 𝑛, for whichmodular arithmetic is well defined. Compute the sum, difference,and product of 12 and 18 mod 25.