Logic Notation question (specifically about logical equivalences) 
$$\text{Equivalence}$$
$p \land T \equiv p\tag{Identity law 1}$
$$p\lor F \equiv p\tag {Identity law 2}$$
$$p\lor T \equiv T\tag{Domination law 1}$$
$$p\land F \equiv F\tag{Domination law 2}$$
So, in the above image, where the T and F are, I assume these represent something like:
T = "any true proposition"
F = "any false proposition" 
And so the first row in English would be "If P and any true proposition is true then this is logically equivalent to P" is that right? I could imagine it being something a bit different. 
Thanks in advance!

You're basically right, though I would very slightly change the wording:
Let $T$ be a true proposition. Let $F$ be a false proposition.
$p \land T \equiv p$: We interpret this as:

The proposition "$p$ is true and $T$ is true" is equivalent to the proposition "$p$ is true."

$p \lor F \equiv p$: We interpret this as:

The proposition "$p$ is true or $F$ is false" is equivalent to the proposition "$p$ is true."

$p \lor T \equiv p$: We interpret this as:

The proposition "$p$ is true or $T$ is true" is equivalent to the proposition "$T$ is true."

$p \land F \equiv p$: We interpret this as:

The proposition "$p$ is true and $F$ is false" is equivalent to the proposition "$F$ is false."

To see why this works, write out the truth tables of each proposition and see that the equivalences do hold.
