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Write which of the following statement are true? Justify your answer.
The sets A = {x : x is a letter of the word "LITTLE"} and,B = {x : x is a letter of the word "TITLE"} are equal.
Concept: undefined >> undefined
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[a \subset A\]
Concept: undefined >> undefined
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Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[\left\{ a, b, e \right\} \subset A\]
Concept: undefined >> undefined
Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true? \[\left\{ 1 \right\} \in A\]
Concept: undefined >> undefined
Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\]Which of the following are true?\[\left\{ 2 \left\{ 1 \right\} \right\} \not\subset A\]
Concept: undefined >> undefined
Write down all possible subsets of each of the following set:
\[\left\{ \phi \right\}\]
Concept: undefined >> undefined
Find the conjugate of the following complex number:
4 − 5 i
Concept: undefined >> undefined
Find the conjugate of the following complex number:
\[\frac{1}{3 + 5i}\]
Concept: undefined >> undefined
Find the conjugate of the following complex number:
\[\frac{1}{1 + i}\]
Concept: undefined >> undefined
Find the conjugate of the following complex number:
\[\frac{(3 - i )^2}{2 + i}\]
Concept: undefined >> undefined
Find the conjugate of the following complex number:
\[\frac{(1 + i)(2 + i)}{3 + i}\]
Concept: undefined >> undefined
Find the conjugate of the following complex number:
\[\frac{(3 - 2i)(2 + 3i)}{(1 + 2i)(2 - i)}\]
Concept: undefined >> undefined
Find the modulus of \[\frac{1 + i}{1 - i} - \frac{1 - i}{1 + i}\].
Concept: undefined >> undefined
Find the modulus and argument of the following complex number and hence express in the polar form:
1 + i
Concept: undefined >> undefined
Find the modulus and argument of the following complex number and hence express in the polar form:
\[\sqrt{3} + i\]
Concept: undefined >> undefined
Find the modulus and argument of the following complex number and hence express in the polar form:
1 − i
Concept: undefined >> undefined
Find the modulus and argument of the following complex number and hence express in the polar form:
\[\frac{1 - i}{1 + i}\]
Concept: undefined >> undefined
Find the modulus and argument of the following complex number and hence express in the polar form:
\[\frac{1}{1 + i}\]
Concept: undefined >> undefined
Find the modulus and argument of the following complex number and hence express in the polar form:
\[\frac{1 + 2i}{1 - 3i}\]
Concept: undefined >> undefined
Find the modulus and argument of the following complex number and hence express in the polar form:
sin 120° - i cos 120°
Concept: undefined >> undefined
