Question

Let p denotes ‘It rains’ q denotes ‘The

atmospheric humidity increases’. Write the

following statements in symbolic form.

(i) Atmospheric humidity increases only if it

rains.

(ii) Sufficient condition for it to rain is that

atmospheric humidity increases

(iii) Necessary condition for it to rain is that

atmospheric humidity increases.

(iv) Whenever atmospheric humidity

increases it rains.

​

Answer 1

Answer:

Solution : p : It rains

q : Atmospheric humidity increases

(a) Given statement is 'atmospheric humidity increases only if it rains'.

∴ It is q only if p.

Symbolically it is q → p.

(b) Given statement is 'sufficient condition for it to rain is that atmospheric humidity

increases'.

∴ It is q is sufficient for p.

Symbolically it is q → p.

(c) Given statement is 'necessary condition for it to rain is that atmospheric humidity

increases'.

∴ It is q is necessary for p.

Symbolically it is p → q.

(d) Given statement is 'whenever atmospheric humidity increases it rains'.

∴ It is p whenever q.

Symbolically it is q → p.

Step-by-step explanation:

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