Which of the following are true of false?
(i) (2 + 3) ! = 2 ! + 3!
(ii) (2 × 3)! = (2!) × (3!)
Option (i) and (ii) both are false
Proofs :
For option (i),
L.H.S. = (2 + 3)! = (5!) = 120
R.H.S. = (2!) + (3!) = 2 + 6 = 8
∴L.H.S. ≠R.H.S.
For option (ii),
L.H.S. = (2 × 3)! = (6!) = 720
R.H.S = (2!) × (3!) = 4 × 6 = 24
∴L.H.S. ≠R.H.S.
Important Notes : for any two whole numbers a and b,
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