For the statement “If P is true then Q is false.” Antecedent is (a) P is true (b) P is not true (c) Q is false (d) Q is not false
Hint: To solve the given question, we will first find out what a statement is and then we will find what type of statement is given in the question. Then, we will divide the given complex statement into two independent statements. Then, we will make use of the fact that the antecedent is the earlier part of the conditional statement. On the basis of this, we will determine the antecedent statement of the given statement.
Complete step-by-step answer: Before we start to solve the given question, we will first find out what statement is. A statement is a sentence that is either true or false but not both. Now, the statement given in the question is a conditional statement. A conditional statement is a statement that is written in the form of “If A then B”. In our case, A is “P is true” and B is “Q is false”. Now, we have to find the antecedent of the given statement. We know that the antecedent of a conditional statement is the earlier part of the statement, i.e. if a conditional statement is of the form “If A then B”, then A will be the antecedent. In our case, A is “P is true”. So, the antecedent in our case will be “P is true”. Hence, option (a) is the right answer.
Note: To find the antecedent of any statement, the statement given should be a conditional statement, i.e. the given statement should be of the form, “If P then Q”. If the given statement is not of this form, then the antecedent of the statement does not exist.
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