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Introduction to Numbers

State whether...

Question

State whether the following statement is true or false? Justify your answer.

(iv) The set of all real numbers is contained in the set of all complex numbers.

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Solution

Since, every real number can be represented in

the form of $a + i b$ .

Therefore, the set of all real numbers is contained in the set of all complex numbers.
Thus, given statement is true.

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Similar questions

Q. Write which of the following statements are true? Justify your answer.
(i) The set of all integers is contained in the set of all set of all rational numbers.
(ii) The set of all crows is contained in the set of all birds.
(iii) The set of all rectangle is contained in the set of all squares.
(iv) The set of all real numbers is contained in the set of all complex numbers.
(v) The sets P = {a} and B = {{a}} are equal.
(vi) 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.

Write which of the following statements are true ? Justify your answer.

(i) The set of all intergers is contained in the set of all rational numbers.

(ii) The set of all crows is contained in the set of all birds.

(iii) The set of all rectangles is contained in the set of all squares.

(iv) The set of all real numbers is contained in the set of all complex numbers.

(v) The sets P = {a} and B = {{a}} are equal.

(vi) 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.

Question 1 (i)
State whether the following statement is true or false. Justify your answer.

Every irrational number is a real number.

Question 1 (iii)
State whether the following statement is true or false. Justify your answer.

Every real number is an irrational number.

State whether the following statement is true or false? Justify your answer.

(i) The set of all integers is contained in the set of all rational numbers

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Introduction to Numbers

Standard VI Mathematics

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