Decide whether the following predicate wffs is valid or inva

Decide whether the following predicate wffs is valid or invalid. If it is valid explain why; and if, it is invalid give an interpretation to justify your answer. P(a) rightarrow (x) P(x)

Solution

The statement is FALSE, since P(a) doesn\'t imply that the given thing will hold for every x belonging to P(x)

Example

Let us assume that the height of five children are given below as (heights in cms)

145 155 165 175 185

Let P be defined as student with height less than 180 cm, then the P(a) will be satisfied for (145,155,165,175) but actually it is not true for all x, hence the given statement is FALSE