Write the following in roster form.
The set of all positive roots of the equation (x-1)(x+1)(x²-1) = 0.

Write the following in roster form.
\(\left\{ x:\frac { x-4 }{ x+2 } =3,x\in R-\{ -2\} \right\} \)

State whether the following sets are finite or infinite.
{x \(\in \) N:x is a rational number}

By taking suitable sets A, B, C, verify the following results:
A \(\times\) (B\(\cup \)C) = (A\(\times\)B) \(\cup \) (A\(\times\)C)

Discuss the following relations for reflexivity, symmetricity and transitivity :
Let A be the set consisting of all the female members of a family. The relation R defined by "aRb if a is not a sister of b".

The distance of an object falling is a function of time t and can be expressed as s(t) = -16t². Graph the function and determine if it is one-to-one.

If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, find \(n((A\cup B)\times(A\cap B)\times(A \triangle B))\)

Simplify \({ 16 }^{ -\frac { 3 }{ 4 } }\)

Simplify \(\left( 3^{ -6 } \right) ^{ \frac { 1 }{ 3 } }\)

Represent the following inequalities in the interval notation:
\(x\le 5\) and \(x\ge -3\)

Solve 23x < 100 when
(i) x is a natural number
(ii) x is an integer.

Find the logarithm of 1728 to the base 2\(\sqrt{3}\)

Identify the quadrant in which an angle of each given measure lies; 25⁰

Identify the quadrant in which an angle of each given measure lies; -55⁰

Identify the quadrant in which an angle of each given measure lies; -230⁰

Prove that \(\cos { \left( 30^o+x \right) } =\frac { \sqrt { 3 } \cos { x } -\sin { x } }{ 2 } \)

Prove that \(\sin { \left( \pi +\theta \right) } =-\sin { \theta } \)

Find the principal value of sec^-1\(\left( -\sqrt { 2 } \right) \)

Prove that \(\sin { 4\alpha } =4\tan { \alpha } \frac { 1-\tan ^{ 2 }{ \alpha } }{ { \left( 1+\tan ^{ 2 }{ \alpha } \right) }^{ 2 } } \)

Express each of the following as a sum or difference. sin 4x cos 2x

Find the value of tan 120°.

Determine whether the following functions are even, odd or neither.
sin (cos(x)).