Kinds and Forms of Proposition

Introduction :

                  A proposition is a sentence expressing something true or false. In philosophy, particularly in logic, a proposition is identified as an idea, concept, or abstraction whose token instances are patterns of symbols, marks, sounds, or strings of words. Propositions are considered to be syntactic entities and also truth bearers.
(Source: Wikipedia)

   In this article, we shall disscuss about kinds and forms of proposition. Also we shall solve problems regarding kinds and forms of propositions.

 

Kinds and forms of propositions:

 

There are two types of propositions

  1. Simple proposition

  2. Compound proposition

1. Simple proposition:

A propositions consisting of just one subject and one predicate is called a simple proposition.

            Example: The following are simple proposition

                                1. Ram is blind.

                                2. Line L and L’ are parallel.

                                3. The flower is not red.

 2.  Compound proposition

            A proposition consisting of two or more simple propositions in the form of a single sentence is called a compound proposition.

             Example: The following are compound propositions,

                         Quadrilateral ABCD is a square and each side of this quadrilateral is 4cm long.

 

Example problem for kinds and forms of proposition:

 

Problem 1:

           Verify 4: 3 = 8: 6 is a proportion or not.

Solution:

           Product of extremes = 4 × 6 = 24

           Product of means = 3 × 8 = 24

                           24 = 24

          These two products are equal.

                   4: 3 = 8: 6 is a proportion.

 Problem 2:

              If 2: 5 = 6: X is a proportion, find the missing term.

Solution:

                  Product of extremes = 2 × x

                  Product of means = 5 × 6 = 30.

                  Since it is a proportion, 2 × x = 30

                  Divide both sides by 2

                   (2 × x) / 2 = `30 / 2`

                                 x =`30 / 2` = 15.

 

Problem 3:

                   The income and Savings of a family are in the ratio 7: 2. If the income of the family is Rs. 5,600. Find how much is being saved.

Solution:

                   Let the savings be Rs. x.

                  The proportion is 7: 2 = 5600: x

                  (Income: Saving) = (Income: Saving)

                                            7x = 2 × 5600

                                      7x / 7 = `(2 (5600)) / 7` = 1600

                                              x = 1600

                         The Savings = Rs.1600.

Problem 4:

                If the cost of 7m cloth is Rs. 49, find the cost of 5m cloth.

                      Quantity(in m) Cost (in Rs.)

                              7                     49

                              5                      ?

Solution:

                The proportion is

                                 7: 5 = 49: ?

                         Product of means = 5 * 9 = 245

                        Product of Extremes = 7 * x

                                                    7 * × = 245

                                           `(7 * x) / 7` = `245 / 7`

                                                         X = `245 / 7`

                                                         X = 35

                           The cost of 5 m cloth = Rs. 35