**Q: How do I make truth tables?!?**

# Category: Logic

## Discrete Logic

**Q: Show that if seven integers are chosen from the first 10 positive integers, there must be at least two pairs with the sum of 11.**

## Scrambling

OK. I must redeem myself in the realm of counting! Too many hasty errors on my last post for discrete math and not enough “thinking.” Don’t fall victim to this. And now to the question:

**Q: How many bit strings (reminder: a bit is either 0 or 1) of length 10 have:
**

**(a) Exactly 3 zeros?
(b) Have the same number of 0 and 1
(c) Have at least 7 zeros
(d) Have at least 3 ones?**