Symbol Operations in Logical Reasoning

This is probably one of the easiest and the most scoring area in the Logical reasoning section of any aptitude-based test. Normally, questions from symbols and operations are asked in sets of 3 - 5 questions. So, you can fetch easy marks in a short span of time. Lately, this topic is gaining importance as a large number of questions in Logical Reasoning section are being asked from it.
Basic Concepts in Symboperation:
For better understanding of this topic, some basic concepts have been explained below:
  • If A = 50 and B = 60, then, is A > B? - of course not.
  • If A = (50, 60) and B = (40, 50), then, is A ≥ B? - This is true, since, A is equal to B when both are 50, else A will always be greater than B.
  • If A = 30 and B = 80, then, is A < B? - Of course yes.
  • If A = (50, 60) and B = (40, 50), then, is A ≤ B? - This is false, as A is equal to B when both are 50, but A > B for all other values. Hence, it should be represented as A ≥ B instead of A ≤ B.
  • If A = B and A > C, then, is B > C? - Of course yes.
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Solved Examples on Symboperation:
DIRECTIONS: The symbols %,?,$, #, and ! are used with the following meaning:
A % B = A is greater than B. A ? B = A is either greater than or equal to B.A $ B = A is smaller than B. A # B = A is either smaller than or equal to B. A ! B = A is equal to B.
Now, for each of the questions mark your answer options as follows:
  • If only conclusion I is true
  • If only conclusion II is true
  • If both conclusion I and II are true
  • If either conclusion I or II is true
  • If neither conclusion I nor II is true
Example 1: Statements: S% T, U $ S, T $ S, S ? M, Q ? R.
Conclusions:
I. T % U
II. M # T
Solution: Firstly, the statements and conclusions should be converted into the normal symbols for better understanding.
Statements: S &gt; T, U &lt; S, T &lt; S, S ≥ M, Q ≥ R.
Conclusions:
I. T > U
II. M ≤ T
Conclusion 1: Since, S > T and U < S. So, U < S > T and, thus, U can be < T or = T or > T. Hence, nothing can be said definitely.
Conclusion 2: Since, T &lt; S and S ≥ M. So, T &lt; S ≥ M. Here again, nothing can be concluded about the relation of M and T.
Hence, the answer is option (e).
Example 2: Statements: T $ Q, S ? M, Q ? R, U $ S, S $ T
Conclusions:
I. Q % S
II. U $ T
Solution: Firstly, the statements and conclusions should be converted into the normal symbols for better understanding of the same.
Statements:T &lt; Q, S ≥ M, Q ≥ R, U &lt; S, S &lt; T.
Conclusions:
I. Q > S
II. U < T
Conclusion 1: Since, T < Q and S < T. So, S < T < Q. Thus, Q > S can be concluded.
Conclusion 2: Since U < S and S < T. So, U < S < T. Thus, conclusion 2 i.e. U < T is definitely true.
Hence, the answer is option (c).
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Symboperations: Key Learning
  • Though the topic is easy to solve, yet practising these questions will make you more confident and you will be able to score good.
  • Before attempting the question, understand the meaning of each operation carefully.
Still in doubt about any concept or example? Don't hesitate, post in the comment section below.