WASSCE Core Mathematics · Paper 1 style

Logical reasoning

One sample question with the full working. 3 more in the app, with instant feedback and repair sessions for the traps below.

Which statement is logically equivalent to 'If it rains, the ground is wet'?

AIf it does not rain, the ground is not wet
BIf the ground is wet, it rained
CIt rains and the ground is not wet
DIf the ground is not wet, it did not rain

Show the answer and working

Answer: D

This is the contrapositive (¬q → ¬p), which is equivalent to p → q.

Trap A Logical reasoning errors: For 'If p then q': the CONTRAPOSITIVE 'If not q then not p' is equivalent; the converse 'If q then p' and inverse 'If not p then not q' are not. The negation of 'All A are B' is 'Some A are not B'.

Trap B Swaps two things that must stay in order: Keep order explicit: (x, y); 'bearing of Q from P' starts at P; in p → q the condition comes first. Label each part before you write the answer.

Trap C Applies the rule for a different situation: Identify the situation first (angle at centre? opposite angles of a cyclic quadrilateral? reverse bearing?) and write the rule that belongs to it before calculating.

Traps in Logical reasoning

Logical reasoning errors
For 'If p then q': the CONTRAPOSITIVE 'If not q then not p' is equivalent; the converse 'If q then p' and inverse 'If not p then not q' are not. The negation of 'All A are B' is 'Some A are not B'.
Swaps two things that must stay in order
Keep order explicit: (x, y); 'bearing of Q from P' starts at P; in p → q the condition comes first. Label each part before you write the answer.
Applies the rule for a different situation
Identify the situation first (angle at centre? opposite angles of a cyclic quadrilateral? reverse bearing?) and write the rule that belongs to it before calculating.
Confuses direct and inverse variation
'Varies directly' → y = kxⁿ (y grows with x). 'Varies inversely' → y = k/xⁿ (y shrinks as x grows). Write the equation from the words first.
Gives the other person's share
Write the ratio with names above the numbers (Kofi : Ama = 4 : 5) and circle whose share is asked for before calculating.

Practise Logical reasoning (3 questions)Send to your class on WhatsApp