If A, B, C are three sets such that A , then prove that C - B - A… - Vidyadip

Question

If A, B, C are three sets such that $\text{A}\subset\text{B},$ then prove that $\text{C} - \text{B}\subset\text{C} - \text{A}.$

✓

Answer

We have, ACB To show: $\text{C} - \text{B}\subset\text{C} - \text{A}$ Let, $\text{x}\in\text{C} - \text{B}$ $\Rightarrow\text{x} \in \text{C and x}\not\in\text{B}$ $\Rightarrow\text{x} \in \text{C and x}\not\in\text{A}$ $[\because \text{A} \subset \text{B}]$ Thus, $\text{x} \in \text{C} - \text{B}\Rightarrow\text{x}\in \text{C} - \text{A}$ This is true for all $\text{x}\in\text{C} - \text{B}$ $\therefore \text{C} - \text{B} \subset \text{C} - \text{A}.$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 4 marks)" from Sets→Sets — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $z_1, z_2$ are two complex numbers such that $|\text{z}_1|=|\text{z}_2|$ and $\text{arg(z}_1)+\text{arg(z}_2)=\pi,$ then show that $\text{z}_1=-\bar{\text{z}}_2.$

Find the equation to the ellipse in the following case:Length of major axis 26, foci $(\pm5, 0)$

Solve the following system of equations in R. $\Big|\frac{3\text{x}-4}{2}\Big|\leq\frac{5}{12}$

In the triangle ABC with vertices A(2, 3), B (4, -1) and C (1, 2) find the equation and length of altitude from the vertex A.

Prove the following identities: $\Big(\frac{1}{\sec^2\text{x}-\cos^\text{x}}+\frac{1}{\text{Cosec}^2\text{x}-\sin^2\text{x}}\Big)\sin^2\text{x}\cos^2\text{x}=\frac{1-\sin^2\text{x}\cos^2\text{x}}{2+\sin^2\text{x}\cos^2\text{x}}$

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): $\frac{\sin\text{x}+\cos\text{x}}{\sin\text{x}-\cos\text{x}}$

Find the equation of the hyperbola whose Vertices are (-8, -1) and (-4, 4) and focus is (17, -1)

Planes are drawn through the points (5, 0, 2) and (3, -2, 5) parallel to the coordinate planes. Find the lengths of the edges of the rectangular parallelopiped so formed.

Prove that $\cos\alpha+\cos(\alpha+\beta)+\cos(\alpha+2\beta)+...+\cos(\alpha+(\text{n}-1)\beta)\\=\frac{\cos\Big\{\alpha+\big(\frac{\text{n}-1}{2}\big)\beta\Big\}\sin\big(\frac{\text{n}\beta}{2}\big)}{\sin\frac{\beta}{2}}$ For all $\text{n}\in\text{N}.$

If the lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents to a circle, then find the radius of the circle.