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If an ability would produce one or more mana of an undefined type, it produces no mana instead.

Some abilities produce mana based on the type of mana another permanent or permanents “could produce.” The type of mana a permanent could produce at any time includes any type of mana that an ability of that permanent would produce if the ability were to resolve at that time, taking into account any applicable replacement effects in any possible order. Ignore whether any costs of the ability could or could not be paid. If that permanent wouldn’t produce any mana under these conditions, or no type of mana can be defined this way, there’s no type of mana it could produce.

To “tap [a permanent] for mana” is to activate a mana ability of that permanent that includes the {T} symbol in its activation cost. See rule 605, “Mana Abilities.”

An ability that triggers whenever a permanent “is tapped for mana” or is tapped for mana of a specified type triggers whenever such a mana ability resolves and produces mana or the specified type of mana.

A replacement effect that applies if a permanent “is tapped for mana” or tapped for mana of a specific type and/or amount modifies the mana production event while such an ability is resolving and producing mana or the specified type and/or amount of mana.

If an object’s enters-the-battlefield triggered ability or replacement effect refers to X, and the spell that became that object as it resolved had a value of X chosen for any of its costs, the value of X for that ability is the same as the value of X for that spell, although the value of X for that permanent is 0. This is an exception to rule 107.3i.

The tap symbol is {T}. The tap symbol in an activation cost means “Tap this permanent.” A permanent that’s already tapped can’t be tapped again to pay the cost. A creature’s activated ability with the tap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

The untap symbol is {Q}. The untap symbol in an activation cost means “Untap this permanent.” A permanent that’s already untapped can’t be untapped again to pay the cost. A creature’s activated ability with the untap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

If a permanent you control is both a creature and a planeswalker, Ajani’s second ability will put both a +1/+1 counter and a loyalty counter on it.

You may activate the first ability with no targets. If you do, you simply put a loyalty counter on Ajani to pay the cost of the ability.

The emblem’s ability doesn’t consider who controls the source dealing damage to you or a planeswalker you control.

Each attacking creature is a separate source of damage. For example, if two 3/3 creatures attack you and are unblocked, the emblem will prevent 2 damage from each creature. You’ll be dealt a total of 2 damage.

If multiple effects modify how damage is dealt, the player being dealt damage or the controller of the permanent being dealt damage chooses the order to apply the effects. For example, Dictate of the Twin Gods says, “If a source would deal damage to a permanent or player, it deals double that damage to that permanent or player instead.” Suppose you would be dealt 3 damage while Dictate of the Twin Gods is on the battlefield and you control Ajani’s emblem. You can either (a) prevent all but 1 damage first and then let Dictate of the Twin Gods’s effect double that, for a result of being dealt 2 damage, or (b) double the damage to 6 and then prevent all but 1 of that damage.