IGDTUW 2026 — Mathematics PYQ

Step 1: Understand Set $A$

The set $A$ is given directly in roster form:

$$A=\{1,3,4\}$$

Step 2: Simplify Set $B$

The set $B$ is given in set-builder form. To find its elements, we need to solve the quadratic equation:

$$x^2-7x+12=0$$

We can solve this by splitting the middle term:

$$x^2-4x-3x+12=0$$

$$x(x-4)-3(x-4)=0$$

$$(x-3)(x-4)=0$$

This gives the roots:

$$x=3\text{or}x=4$$

Therefore, writing set $B$ in roster form gives:

$$B=\{3,4\}$$

Step 3: Analyze the relationship between Set $A$ and Set $B$

Now, let's compare both sets:

• $$A=\{1,3,4\}$$

• $$B=\{3,4\}$$

• Checking option (a): Every element of $A$ is not in $B$ (since $1\in A$ but $1\notin B$). So, $A$ is not a subset of $B$ ($A⊈B$).

• Checking option (b): Every element of $B$ (which are $3$ and $4$) is also present in set $A$. Therefore, $B$ is a subset of $A$ ($B\subseteq A$).

• Checking option (c): Since the elements are not exactly the same, $A\ne B$.

• Checking option (d): Equivalent sets must have the same number of elements. Here, $n(A)=3$ and $n(B)=2$. Since $3\ne 2$, they are not equivalent.

Correct Answer

(b) $B$ is a subset of $A$