Question

16. 5 The following are true except (a) If every element of a set B is an element of a set A, then B is a subset of A. (b) A is a subset of B is denoted by A⊂B (c) Two sets A and B are equal if and only if A⊆B and B⊆A (d) Two sets A and B are equal if and only if A = -B and B = A
17. If A = { a + i b / a, b ϵ R }, then A is a set of ……… numbers (a) rational (b) natural (c) real (d) complex

Answer 1

Answer on Question #54797 – Math – Abstract Algebra

16 The following are true except

(a) If every element of a set $B$ is an element of a set $A$, then $B$ is a subset of $A$.

(b) $A$ is a subset of $B$ is denoted by $A \subset B$

(c) Two sets $A$ and $B$ are equal if and only if $A \subseteq B$ and $B \subseteq A$

(d) Two sets $A$ and $B$ are equal if and only if $A = -B$ and $B = A$

17 If $A = \{a + i b \mid a, b \in \mathbb{R}\}$, then $A$ is a set of ... numbers

(a) rational (b) natural (c) real (d) complex

Solution

16 The following are true except (d). Counterexample: $A = \{1,2\} = B$. But $-B = \{-1,-2\} \neq A$

17 The definition of the complex number is the following:

a complex number is a number that can be expressed in the form $a + bi$, where $a$ and $b$ are real numbers and $i$ is the imaginary unit, that satisfies the equation $i^2 = -1$.

In the expression $a + bi$, $a$ is the real part and $b$ is the imaginary part of the complex number $a + bi$.

Answer:

16 (d)

17 (d)

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