INDUCTIVE & DEDUCTIVE
REASONING
MATHEMATICS IN THE MODERN WORLD
1
1. For all the numbers X, X > FALSE
X
Soln.
1
X = 2, 2 > X = 1, 1 > 1
2
1 1
X = 6, 6 > X = -6, -6 > OR 0.17
6 -6
1 1 1
X = 1080, 1080 > X= , >2
1080 2 2
COUNTEREXAMPLES
2. For all the numbers X, X + X > X FALSE
Soln.
X = 2, 2 + 2 > 2 X = -8, (-8) + (-8) > -8
=4>2 = -16 > -8
X = 16, 16 + 16 > 16 X = -1080, (-1080) + (-1080) > -1080
= 32 > 16 = -2,160 > -1,080
X = 1, 1 + 1 > 1
=2>1
COUNTEREXAMPLES
REASONING
MATHEMATICS IN THE MODERN WORLD
1
1. For all the numbers X, X > FALSE
X
Soln.
1
X = 2, 2 > X = 1, 1 > 1
2
1 1
X = 6, 6 > X = -6, -6 > OR 0.17
6 -6
1 1 1
X = 1080, 1080 > X= , >2
1080 2 2
COUNTEREXAMPLES
2. For all the numbers X, X + X > X FALSE
Soln.
X = 2, 2 + 2 > 2 X = -8, (-8) + (-8) > -8
=4>2 = -16 > -8
X = 16, 16 + 16 > 16 X = -1080, (-1080) + (-1080) > -1080
= 32 > 16 = -2,160 > -1,080
X = 1, 1 + 1 > 1
=2>1
COUNTEREXAMPLES