#Mike# First, notice that Mary 3 and Mike 1 cannot both be true: they disagree on the bag that went to Houston.

#Mary, Jeff, and Katie# Now notice that both Katie 5 and Jeff 3 cannot both be true: one of them must be false because of Mike 3 being true.

#Jeff#

#Rebecca and Alan# Looking at Rebecca 4, it is quite the load of info. If we assume it is true, then this ends up being Mike. Since he is not on concourse F, we know the United flight must be based on Mary 2. This gets us here.

#Finishing Up# We now know all the false statements:

Mike

First, notice that Mary 3 and Mike 1 cannot both be true: they disagree on the bag that went to Houston.

Mary, Jeff, and Katie

Now notice that both Katie 5 and Jeff 3 cannot both be true: one of them must be false because of Mike 3 being true.

Jeff

Rebecca and Alan

Looking at Rebecca 4, it is quite the load of info. If we assume it is true, then this ends up being Mike. Since he is not on concourse F, we know the United flight must be based on Mary 2. This gets us here.

Finishing Up

We now know all the false statements:

1:

Mary    Dallas      Las Vegas       Green   JetBlue     C
Jeff    Orlando     Miami           Red     Delta       A
Allan   Los Angeles Phoenix         White   American    B
Mike    Chicago     Houston         Black   United      F
Rebecca Denver      Charlotte       Blue    Southwest   E
Katie   New York    San Francisco   Brown   Frontier    D

2:

Mary    Dallas      Las Vegas       Green   JetBlue     C
Jeff    Orlando     Miami           Red     Delta       A
Allan   Los Angeles Phoenix         White   American    B
Mike    New York    Houston         Black   United      F
Rebecca Denver      Charlotte       Blue    Southwest   E
Katie   Chicago     San Francisco   Brown   Frontier    D

3:

Mary    Dallas      Las Vegas       Green   JetBlue     C
Jeff    Orlando     Miami           Red     Delta       A
Allan   Los Angeles Phoenix         White   American    F
Mike    Chicago     Houston         Black   United      B
Rebecca Denver      Charlotte       Blue    Southwest   E
Katie   New York    San Francisco   Brown   Frontier    D

This makes Allan 5 false, so Allan 1,2,3,4 are all true and we get here.

#Finishing Up# We now know all the false/true statements.

This makes Allan 5 false, so Allan 1,2,3,4 are all true and we get here.

#Finishing Up# We now know all the false statements:

• Mary 1
• Jeff 5
• Allan 5
• Mike 1
• Rebecca 4
• Katie 5

The rest are true. Of these, there are a few that we haven't been able to fully realize in the truth table. There are no obvious things that can be done in the truth table. These are:

• Mary 2
• Jeff 2,
• Allan 1, 3
• Mike 3, !Mike 1

We have to make sure truth (or falsehood) of these statements is maintained.

Lets try Allan on concourse B. This puts Mike on F, which makes him fly United from Mary 2.

Now it we try Mike coming out of Chicago, then the puzzle is solved(1)! Turns out if we try Mike out of New York, solved(2)!

So now lets try Allan on F instead. From Jeff 2, we know that Chicago must be out of concourse B. Since this puts F on America, Mike must fly United from Mary 2. This yields another solution(3)

So, there are 3 solutions to this puzzle based on these clues.