Hi Ajit, I'll try to help!
A conditional statement, in its simplest form, is "if this, then that." For example, if I am invited to the party, I will go to the party. We can diagram this relationship as follows:
Invited to Party

Go to Party
The contrapositive of a conditional statement is what you get when we say we don't have that second part (the "necessary condition"), and therefore we cannot have that first part (the "sufficient condition") Thus, if I now tell you that I will not be going to the party, you can infer that I was not invited. That can be diagrammed as:
Go to Party
Invited to Party
The strikethroughs of those terms can be read as negations of the terms. This means "if I don't go to the party, then I was not invited to the party." We know the contrapositive must be true, because the original statement meant I was absolutely going to go to the party if I was invited. You'll hear and see the phrase "reverse and negate" in relation to diagramming the contrapositive, and you can see that the diagram does exactly that.
Now, let's say I also said "If I am invited to the party, I will buy a nice bottle of wine to bring to the host."
Now, my being invited to the party is sufficient to prove two different things: I will go to the party, and I will buy a nice bottle of wine to bring to the host. We can combine those statements into one, like this:
Invited to Party

Go to Party AND Buy Wine
In the argument, we knew that if you don't read history books, then you don't know history. The contrapositive of that is if you do know history, you do read history books. Reverse and negate that claim to create this new way of looking at the relationship. And then, we can combine the two statements into one!
Know History

Easy to Impress
Know History

Read History Books
Combined into one:
Know History

Easy to Impress AND Read History Books
Finally, here's a similar setup to the premises in the stimulus:
If you don't have a passport, you cannot board an international flight.
If you are allowed to board an international flight, you must have a boarding pass.
Combine the contrapositive of the first sentence with the second sentence, and we get:
If you are allowed to board an international flight, you have a boarding pass and a passport, or:
Allowed to Board

Boarding Pass AND Passport
I hope that helps! If you are unfamiliar with conditional reasoning, start looking into it asap, as it is one of the most commonly tested forms of reasoning in the Logical Reasoning sections on the LSAT. It's covered in the LR Bible, in some of our free webinars, and of course, in our courses.
Adam M. Tyson
PowerScore LSAT, GRE, ACT and SAT Instructor
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