Bissoy.com
Doctors Medicines MCQs Q&A

What is the correct translation of the following statement into mathematical logic? “Some real numbers are rational”

What is the correct translation of the following statement into mathematical logic? “Some real numbers are rational” Correct Answer ∃x (real(x) ∧ rational(x)) 

The correct answer is option 3.

STATEMENT:

“Some real numbers are rational”

Option 1: Incorrect

There exist some numbers which are either real OR rational

Option 2: Incorrect

All real numbers are rational

Option 3: Correct

There exist some numbers which are both real and rational

Option 4: Incorrect

There exists a number such that if it is rational, it is real​

Related Questions

Consider the following numbers: 1. Every irrational number is a real number. 2. Every real number is a rational number. 3. Every rational number is a real number. 4. Every integer is a real number. Which of the above statements are correct?
In this question two statements and two conclusions i and ii have been given. You have to consider both the conclusions by considering the statement as true and deciding which conclusions are logically logical beyond any doubt. Statement: All balls are bat. All bats are rubber. Conclusion: i) All balls are rubber. ii) There are some rubber balls. Select the correct option from the given options. (A) Only conclusions i is logical (B) Only conclusions ii is rational (C) or conclusions i or ii is rational (D) nor the conclusions ii is rational (E) both the conclusions i and ii are rational
In this question, the relation between different elements is shown in the statement. After the statement, two conclusions are given: Statement: A = N ≤ L < Y > S Conclusion: i) A ≤ L ii) L < S Select the correct option from the given options. (A) Only conclusions i is logical (B) Only conclusions ii is rational (C) or conclusions i or ii is rational (D) nor the conclusions ii is rational (E) both the conclusions i and ii are rational
In this question the relationship between the various elements of the statement is shown. The statement has two conclusions. Statement: M ≤ N < O ≥ P < Q Conclusion: i) M < P ii) O < Q Select the right from the following options. A) The only conclusion I is rational. B) The only conclusion ii is logical. C) either i or ii conclusion is rational. D) neither i nor ii conclusion is rational. E) i and ii both conclusions are rational.
In this question the connection between different elements has been shown in the statement. After the statement two conclusions have been given. Statement: M ≤ N < O ≥ P < Q Conclusion: i) M ≥ P ii) O > M Choose the right from the following options. A) The only conclusion i is rational. B) The only conclusion ii is logical. C) either i or ii conclusion is rational. D) neither i nor ii conclusion is rational. 5) i and ii both conclusions are rational.
A statement in this question and the two conclusions related to them are given in the form of i and ii, assuming that the statements given in the statements to be true are to be considered together on both the findings and to make sure that the information given in the statement Which of the conclusions beyond reasonable doubt is logical? Statement: Every Monday is a working day. Today is a working day. Conclusion: i. Today is Monday. ii. Only Monday is a working day. Choose the right one from the following options: A) The only conclusion is rational. B) The only conclusion ii is logical. C) either i or ii conclusion is rational. D) neither i nor ii conclusion is rational. E) i and ii both conclusions are rational.
Consider the following statements: 1. Every natural number is a real number 2. Every real number is a rational number 3. Every integer is a real number 4. Every rational number is a real number Which of the above statements are correct?
In this question, a statement and related two conclusions have been given in the form of i and ii, assuming that the statements given in the statements to be true are to be sure that what conclusions regarding the statements are logical? Statement: It rains on every Monday, it is raining today. Conclusion: i) It is rainy season. ii) Today is Monday. Choose the right one from the following options. A) The only conclusion i is rational. B) The only conclusion ii is logical. C) either i or ii conclusion is rational. D) neither i nor ii conclusion is rational. E) i and ii both conclusions are rational.
In the question below are given two statements followed by two conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts. Statements: I. Only a few irrational is rational II. No rational is integer Conclusions: I. Some irrational is not rational II. No integer is rational
Two statements in this question and two related findings have been given in the form of i and ii. You should consider the statements given in the statements as valid and to determine which conclusions are relevant in relation to the statements? Statement: All candles are wicker. Some lighter are wicker. Conclusion: i) Some candles are lighter. ii) Some wickers are lighters. Select one of the most suitable in the following options: A. Only conclusion i rational is B. Only conclusion ii is logical C. The conclusions i or ii is logical D. Neither the conclusion i nor ii is rational E. i and ii both conclusions are rational