1. Given the statement: "If a student takes biology, then she is taking science."
(5 marks)
a) Write the inverse of the statement. Is this statement true? (If the statement is false, provide a counterexample.)

Answer

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Answer

Counterexample: A student taking physics or chemistry, which are also science subjects, but not taking biology.

Steps

Step 1 ：Given the statement: 'If a student takes biology, then she is taking science.'

Step 2 ：Let P = 'a student takes biology' and Q = 'she is taking science'.

Step 3 ：The inverse of the statement is 'If not P, then not Q'.

Step 4 ：Substitute P and Q: 'If a student does not take biology, then she is not taking science.'

Step 5 ：\(\boxed{\text{This statement is not necessarily true.}}\)

Step 6 ：Counterexample: A student taking physics or chemistry, which are also science subjects, but not taking biology.