E, I, R, O denote respectively the sets of all equilateral, isosceles, right angled and obtuse angled triangles in a plane, then which of the following is not true.

Question

E, I, R, O denote respectively the sets of all equilateral, isosceles, right angled and obtuse angled triangles in a plane, then which of the following is not true. (A) R ∩ E=φ, R ∩ I ≠ φ (B) E ∩ O=φ, O ∩ I ≠ φ (C) E ∩ I=φ, E ∩ O ≠ φ (D) E ∩ I ≠ φ, E ⊂ I

Tardigrade Admin · Accepted Answer

An equilateral triangle cannot be obtuse angled or right angled but is an isosceles triangle. So E ⊂ I and E ∩ I=E.

Q. $E, I, R, O$ denote respectively the sets of all equilateral, isosceles, right angled and obtuse angled triangles in a plane, then which of the following is not true.

$R \cap E = ϕ, R \cap I \neq = ϕ$

$E \cap O = ϕ, O \cap I \neq = ϕ$

$E \cap I = ϕ, E \cap O \neq = ϕ$

$E \cap I \neq = ϕ, E \subset I$

An equilateral triangle cannot be obtuse angled or right angled but is an isosceles triangle.
So $E \subset I$ and $E \cap I = E$ .

Q. E,I,R,O denote respectively the sets of all equilateral, isosceles, right angled and obtuse angled triangles in a plane, then which of the following is not true.

R∩E=ϕ,R∩I=ϕ

E∩O=ϕ,O∩I=ϕ

E∩I=ϕ,E∩O=ϕ

E∩I=ϕ,E⊂I