Question 36 of 47intermediate🔧 ApplyShort Answer2 marks

Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60°, what is A'?

Correct Answer

Given that U is the universal set of all triangles in a plane, and A is the set of all triangles with at least one angle different from 60°.

The complement of A, denoted by A', is defined as A' = {x : x ∈ U and x ∉ A}. This means A' contains all elements of U that do not belong to A.

Since A contains triangles having at least one angle different from 60°, the complement A' will contain triangles where no angle is different from 60°. This means all three angles must be equal to 60°. Such triangles are equilateral triangles.

Therefore, A' is the set of all equilateral triangles in the plane.

Exercise: EXERCISE 1.5 | Q: 6 | (Page 20)
For More Understanding

Explanation

This question tests the concept of complement of a set. From the textbook context, the complement A' is defined as {x : x ∈ U and x ∉ A}. The key insight is recognizing that if A contains triangles with 'at least one angle different from 60°', then A' must contain triangles where this condition fails - meaning all three angles equal 60°. A triangle with all angles equal to 60° is precisely an equilateral triangle.

Solution Steps

  1. Step 1: Identify U = set of all triangles in a plane (universal set).

  2. Step 2: Identify A = set of triangles with at least one angle ≠\neq 60°.

  3. Step 3: Apply complement definition: A' = {x : x ∈ U and x ∉ A}.

  4. Step 4: Determine what triangles are NOT in A - triangles where all angles = 60°.

  5. Step 5: Conclude: A' = set of all equilateral triangles.

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