B tech. Discrete mathematics (I. T & Comp. Science Engg.) Syllabus


A proposition (or a statement) is a declarative sentence that is either true or false, but not both



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PROPOSITION (OR STATEMENT)

A proposition (or a statement) is a declarative sentence that is either true or false, but not both.

A proposition (or a statement) is a declarative sentence which is either true or false but not both.


Imperative, exclamatory, interrogative or open sentences are not statements in logic.
Example 1 : For Example consider, the following sentences.
  1. VSSUT is at Burla.

(ii) 2 + 3 = 5

  1. The Sun rises in the east.

  2. Do your home work.

  3. What are you doing?

(vi) 2 + 4 = 8

  1. 5 < 4

  2. The square of 5 is 15.

  3. x  3  2
  4. May God Bless you!

All of them are propositions except (iv), (v),(ix) & (x) sentences ( i), (ii) are true, whereas (iii),(iv), (vii) & (viii) are false.


Sentence (iv) is command, hence not a proposition. ( v ) is a question so not a statement. ( ix) is a declarative sentence but not a statement, since it is true or false depending on the value of x. (x) is a exclamatory sentence and so it is not a statement.
Mathematical identities are considered to be statements. Statements which are imperative, exclamatory, i nterrogative or open are not statements in logic.


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