1] Let x,y∈R. Prove that ∀x∀y(4x+9y>9⇒(x>5/4 ∨ y> 4/9)) using method of indirect proof. 2] Let x,y∈R (a). Prove that if

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1] Let x,y∈R. Prove that ∀x∀y(4x+9y>9⇒(x>5/4 ∨ y> 4/9))using method of indirect proof.
2] Let x,y∈R
(a). Prove that if x≥a and y>b, then x+y>a+b using methodof direct proof.
(b). Prove that ∀x∀y(10x+21y>21⇒(x>11/10 ∨y>10/21))
3] Using the proof by case prove that ∀x ∈ Z 25X2−5x+12 iseven
4] Let x, y∈R Using proof by contradiction, prove that∀x∀y(512y3+8X2y≤x3+64y2x⇒8y≤x)
5] Let R be a relation defined on N×N as (a,b)R(c,d) if and onlyif 3bd(a−c)=4ac(d−b). Then show that R is an equivalencerelation.