Thread: true or false . For every number x, x<13 or x>6

have done a million of these types of questions with truth tables and what not, but when asked this way, I am completely stumped:

1. true or false . For every number x, x<13 or x>6

2.For some interger n, n is greater than or equal to 4 and n is less than or equal to 4.


I am especially interested in the first problem. If you can i'd like to see the problem answered rather than clues. Any help appreciated.

Originally Posted by rune2402

1. true or false . For every number x, x<13 or x>6

2.For some interger n, n is greater than or equal to 4 and n is less than or equal to 4.

1. If I give you a number, any number, is it greater that 6?. If not then is it less than 13?
Recall that an ‘or’ is true if at least one of the disjunctives is true.

2. Think about n=4.

I just cannot figure it out because x could be anything. I guess. I know the rule for "or" statements, but I am lost now. I mean numbers 7 - 12 would make both statements true. In which case, the truth value of the equation would be true.

One or both of the individual statements must be true for whole statement to be true. If i substitute the 7-12 for x, then both are ture.

The disjunction ‘or’ is true if at least one of the disjunctives is true.
At least one means one or the other or both: one or two.